Type:	Package
Title:	Package for Environmental Statistics, Including US EPA Guidance
Version:	3.1.0
Date:	2025-04-17
Depends:	R (≥ 3.5.0)
Imports:	MASS, ggplot2, nortest
Suggests:	lattice, qcc, sp, boot, tinytest, covr, Hmisc
Description:	Graphical and statistical analyses of environmental data, with focus on analyzing chemical concentrations and physical parameters, usually in the context of mandated environmental monitoring. Major environmental statistical methods found in the literature and regulatory guidance documents, with extensive help that explains what these methods do, how to use them, and where to find them in the literature. Numerous built-in data sets from regulatory guidance documents and environmental statistics literature. Includes scripts reproducing analyses presented in the book "EnvStats: An R Package for Environmental Statistics" (Millard, 2013, Springer, ISBN 978-1-4614-8455-4, <doi:10.1007/978-1-4614-8456-1>).
License:	GPL (≥ 3)
URL:	https://github.com/alexkowa/EnvStats, https://alexkowa.github.io/EnvStats/
LazyLoad:	yes
LazyData:	yes
NeedsCompilation:	no
Packaged:	2025-04-24 05:09:48 UTC; alex
Author:	Steven P. Millard [aut], Alexander Kowarik [ctb, cre]
Maintainer:	Alexander Kowarik <alexander.kowarik@statistik.gv.at>
Repository:	CRAN
Date/Publication:	2025-04-24 12:00:07 UTC

Trichloroethylene Concentrations Before and After Remedation

Description

Trichloroethylene (TCE) concentrations (mg/L) at 10 groundwater monitoring wells before and after remediation.

Usage

data(ACE.13.TCE.df)

Format

A data frame with 20 observations on the following 3 variables.

TCE.mg.per.L

TCE concentrations

Well

a factor indicating the well number

Period

a factor indicating the period (before vs. after remediation)

Source

USACE. (2013). Environmental Quality - Environmental Statistics. Engineer Manual EM 200-1-16, 31 May 2013. Department of the Army, U.S. Army Corps of Engineers, Washington, D.C. 20314-1000, p. M-10. https://www.publications.usace.army.mil/Portals/76/Publications/EngineerManuals/EM_200-1-16.pdf.

Randomly sampled measurements of an analyte in soil samples.

Description

Analyte concentrations (\mug/g) in 11 discrete environmental soil samples.

Usage

    BJC.2000.df
    data(BJC.2000.df)

Format

A data frame with 11 observations on the following 4 variables.

Analyte.char

Character vector indicating lead concentrations. Nondetects indicated with the letter U after the measure (e.g., 0.10U)

Analyte

numeric vector indicating analyte concentration.

Censored

logical vector indicating censoring status.

Detect

numeric vector of 0s (nondetects) and 1s (detects) indicating censoring status.

Source

BJC. (2000). Improved Methods for Calculating Concentrations Used in Exposure Assessments. BJC/OR-416, Prepared by the Lockheed Martin Energy Research Corporation. Prepared for the U.S. Department of Energy Office of Environmental Management. Bechtel Jacobs Company, LLC. January, 2000. https://rais.ornl.gov/documents/bjc_or416.pdf.

Lead concentration in soil samples.

Description

Lead (Pb) concentrations (mg/kg) in 29 discrete environmental soil samples from a site suspected to be contaminated with lead.

Usage

    Beal.2010.Pb.df
    data(Beal.2010.Pb.df)

Format

A data frame with 29 observations on the following 3 variables.

Pb.char

Character vector indicating lead concentrations. Nondetects indicated with the less-than sign (e.g., <1)

Pb

numeric vector indicating lead concentration.

Censored

logical vector indicating censoring status.

Source

Beal, D. (2010). A Macro for Calculating Summary Statistics on Left Censored Environmental Data Using the Kaplan-Meier Method. Paper SDA-09, presented at Southeast SAS Users Group 2010, September 26-28, Savannah, GA. https://analytics.ncsu.edu/sesug/2010/SDA09.Beal.pdf.

Benthic Data from Monitoring Program in Chesapeake Bay

Description

Benthic data from a monitoring program in the Chesapeake Bay, Maryland, covering July 1994 - December 1991.

Usage

Benthic.df

Format

A data frame with 585 observations on the following 7 variables.

Site.ID

Site ID

Stratum

Stratum Number (101-131)

Latitude

Latitude (degrees North)

Longitude

Longitude (negative values; degrees West)

Index

Benthic Index (between 1 and 5)

Salinity

Salinity (ppt)

Silt

Silt Content (% clay in soil)

Details

Data from the Long Term Benthic Monitoring Program of the Chesapeake Bay. The data consist of measurements of benthic characteristics and a computed index of benthic health for several locations in the bay. Sampling methods and designs of the program are discussed in Ranasinghe et al. (1992).

The data represent observations collected at 585 separate point locations (sites). The sites are divided into 31 different strata, numbered 101 through 131, each strata consisting of geographically close sites of similar degradation conditions. The benthic index values range from 1 to 5 on a continuous scale, where high values correspond to healthier benthos. Salinity was measured in parts per thousand (ppt), and silt content is expressed as a percentage of clay in the soil with high numbers corresponding to muddy areas.

The United States Environmental Protection Agency (USEPA) established an initiative for the Chesapeake Bay in partnership with the states bordering the bay in 1984. The goal of the initiative is the restoration (abundance, health, and diversity) of living resources to the bay by reducing nutrient loadings, reducing toxic chemical impacts, and enhancing habitats. USEPA's Chesapeake Bay Program Office is responsible for implementing this initiative and has established an extensive monitoring program that includes traditional water chemistry sampling, as well as collecting data on living resources to measure progress towards meeting the restoration goals.

Sampling benthic invertebrate assemblages has been an integral part of the Chesapeake Bay monitoring program due to their ecological importance and their value as biological indicators. The condition of benthic assemblages is a measure of the ecological health of the bay, including the effects of multiple types of environmental stresses. Nevertheless, regional-scale assessment of ecological status and trends using benthic assemblages are limited by the fact that benthic assemblages are strongly influenced by naturally variable habitat elements, such as salinity, sediment type, and depth. Also, different state agencies and USEPA programs use different sampling methodologies, limiting the ability to integrate data into a unified assessment. To circumvent these limitations, USEPA has standardized benthic data from several different monitoring programs into a single database, and from that database developed a Restoration Goals Benthic Index that identifies whether benthic restoration goals are being met.

Source

Ranasinghe, J.A., L.C. Scott, and R. Newport. (1992). Long-term Benthic Monitoring and Assessment Program for the Maryland Portion of the Bay, Jul 1984-Dec 1991. Report prepared for the Maryland Department of the Environment and the Maryland Department of Natural Resources by Versar, Inc., Columbia, MD.

Examples

  attach(Benthic.df)

  # Show station locations
  #-----------------------
  dev.new()
  plot(Longitude, Latitude, 
      xlab = "-Longitude (Degrees West)",
      ylab = "Latitude",
      main = "Sampling Station Locations")


  # Scatterplot matrix of benthic index, salinity, and silt
  #--------------------------------------------------------
  dev.new()
  pairs(~ Index + Salinity + Silt, data = Benthic.df)


  # Contour and perspective plots based on loess fit
  # showing only predicted values within the convex hull
  # of station locations
  #-----------------------------------------------------
  library(sp)

  loess.fit <- loess(Index ~ Longitude * Latitude,
      data=Benthic.df, normalize=FALSE, span=0.25)
  lat <- Benthic.df$Latitude
  lon <- Benthic.df$Longitude
  Latitude <- seq(min(lat), max(lat), length=50)
  Longitude <- seq(min(lon), max(lon), length=50)
  predict.list <- list(Longitude=Longitude,
      Latitude=Latitude)
  predict.grid <- expand.grid(predict.list)
  predict.fit <- predict(loess.fit, predict.grid)
  index.chull <- chull(lon, lat)
  inside <- point.in.polygon(point.x = predict.grid$Longitude, 
      point.y = predict.grid$Latitude, 
      pol.x = lon[index.chull], 
      pol.y = lat[index.chull])
  predict.fit[inside == 0] <- NA

  dev.new()
  contour(Longitude, Latitude, predict.fit,
      levels=seq(1, 5, by=0.5), labcex=0.75,
      xlab="-Longitude (degrees West)",
      ylab="Latitude (degrees North)")
  title(main=paste("Contour Plot of Benthic Index",
      "Based on Loess Smooth", sep="\n"))

  dev.new()
  persp(Longitude, Latitude, predict.fit,
      xlim = c(-77.3, -75.9), ylim = c(38.1, 39.5), zlim = c(0, 6), 
      theta = -45, phi = 30, d = 0.5,
      xlab="-Longitude (degrees West)",
      ylab="Latitude (degrees North)",
      zlab="Benthic Index", ticktype = "detailed")
  title(main=paste("Surface Plot of Benthic Index",
      "Based on Loess Smooth", sep="\n"))

  detach("Benthic.df")

  rm(loess.fit, lat, lon, Latitude, Longitude, predict.list,
      predict.grid, predict.fit, index.chull, inside)

Abstract: Castillo and Hadi (1994)

Description

Detailed abstract of the manuscript:

Castillo, E., and A. Hadi. (1994). Parameter and Quantile Estimation for the Generalized Extreme-Value Distribution. Environmetrics 5, 417–432.

Details

Abstract
Castillo and Hadi (1994) introduce a new way to estimate the parameters and quantiles of the generalized extreme value distribution (GEVD) with parameters location=\eta, scale=\theta, and shape=\kappa. The estimator is based on a two-stage procedure using order statistics, denoted here by “TSOE”, which stands for two-stage order-statistics estimator. Castillo and Hadi (1994) compare the TSOE to the maximum likelihood estimator (MLE; Jenkinson, 1969; Prescott and Walden, 1983) and probability-weighted moments estimator (PWME; Hosking et al., 1985).

Castillo and Hadi (1994) note that for some samples the likelihood may not have a local maximum, and also when \kappa > 1 the likelihood can be made infinite so the MLE does not exist. They also note, as do Hosking et al., 1985), that when \kappa \le -1, the moments and probability-weighed moments of the GEVD do not exist, hence neither does the PWME. (Hosking et al., however, claim that in practice the shape parameter usually lies between -1/2 and 1/2.) On the other hand, the TSOE exists for all values of \kappa.

Based on computer simulations, Castillo and Hadi (1994) found that the performance (bias and root mean squared error) of the TSOE is comparable to the PWME for values of \kappa in the range -1/2 \le \kappa \le 1/2. They also found that the TSOE is superior to the PWME for large values of \kappa. Their results, however, are based on using the PWME computed using the approximation given in equation (14) of Hosking et al. (1985, p.253). The true PWME is computed using equation (12) of Hosking et al. (1985, p.253). Hosking et al. (1985) introduced the approximation as a matter of computational convenience, and noted that it is valid in the range -1/2 \le \kappa \le 1/2. If Castillo and Hadi (1994) had used the true PWME for values of \kappa larger than 1/2, they probably would have gotten very different results for the PWME. (Note: the function egevd with method="pwme" uses the exact equation (12) of Hosking et al. (1985), not the approximation (14)).

Castillo and Hadi (1994) suggest using the bootstrap or jackknife to obtain variance estimates and confidence intervals for the distribution parameters based on the TSOE.

More Details Let \underline{x} = (x_1, x_2, \ldots, x_n) be a vector of n observations from a generalized extreme value distribution with parameters location=\eta, scale=\theta, and shape=\kappa with cumulative distribution function F. Also, let x(1), x(2), \ldots, x(n) denote the ordered values of \underline{x}.

First Stage
Castillo and Hadi (1994) propose as initial estimates of the distribution parameters the solutions to the following set of simultaneous equations based on just three observations from the total sample of size n:

F[x(1); \eta, \theta, \kappa] = p_{1,n}

F[x(j); \eta, \theta, \kappa] = p_{j,n}

F[x(n); \eta, \theta, \kappa] = p_{n,n} \;\;\;\; (1)

where 2 \le j \le n-1, and

p_{i,n} = \hat{F}[x(i); \eta, \theta, \kappa]

denotes the i'th plotting position for a sample of size n; that is, a nonparametric estimate of the value of F at x(i). Typically, plotting positions have the form:

p_{i,n} = \frac{i-a}{n+b} \;\;\;\; (2)

where b > -a > -1. In their simulation studies, Castillo and Hadi (1994) used a=0.35, b=0.

Since j is arbitrary in the above set of equations (1), denote the solutions to these equations by:

\hat{\eta}_j, \hat{\theta}_j, \hat{\kappa}_j

There are thus n-2 sets of estimates.

Castillo and Hadi (1994) show that the estimate of the shape parameter, \kappa, is the solution to the equation:

\frac{x(j) - x(n)}{x(1) - x(n)} = \frac{1 - A_{jn}^\kappa}{1 - A_{1n}^\kappa} \;\;\;\; (3)

where

A_{ik} = C_i / C_k \;\;\;\; (4)

C_i = -log(p_{i,n}) \;\;\;\; (5)

Castillo and Hadi (1994) show how to easily solve equation (3) using the method of bisection.

Once the estimate of the shape parameter is obtained, the other estimates are given by:

\hat{\theta}_j = \frac{\hat{\kappa}_j [x(1) - x(n)]}{(C_n)^{\hat{\kappa}_j} - (C_1)^{\hat{\kappa}_j}} \;\;\;\; (6)

\hat{\eta}_j = x(1) - \frac{\hat{\theta}_j [1 - (C_1)^{\hat{\kappa}_j}]}{\hat{\kappa}_j} \;\;\;\; (7)

Second Stage
Apply a robust function to the n-2 sets of estimates obtained in the first stage. Castillo and Hadi (1994) suggest using either the median or the least median of squares (using a column of 1's as the predictor variable; see the help file for lmsreg in the package MASS). Using the median, for example, the final distribution parameter estimates are given by:

\hat{\eta} = Median(\hat{\eta}_2, \hat{\eta}_3, \ldots, \hat{\eta}_{n-1})

\hat{\theta} = Median(\hat{\theta}_2, \hat{\theta}_3, \ldots, \hat{\theta}_{n-1})

\hat{\kappa} = Median(\hat{\kappa}_2, \hat{\kappa}_3, \ldots, \hat{\kappa}_{n-1})

Author(s)

Steven P. Millard (EnvStats@ProbStatInfo.com)

References

Forbes, C., M. Evans, N. Hastings, and B. Peacock. (2011). Statistical Distributions. Fourth Edition. John Wiley and Sons, Hoboken, NJ.

Hosking, J.R.M. (1985). Algorithm AS 215: Maximum-Likelihood Estimation of the Parameters of the Generalized Extreme-Value Distribution. Applied Statistics 34(3), 301–310.

Jenkinson, A.F. (1969). Statistics of Extremes. Technical Note 98, World Meteorological Office, Geneva.

Johnson, N. L., S. Kotz, and N. Balakrishnan. (1995). Continuous Univariate Distributions, Volume 2. Second Edition. John Wiley and Sons, New York.

Prescott, P., and A.T. Walden. (1983). Maximum Likelihood Estimation of the Three-Parameter Generalized Extreme-Value Distribution from Censored Samples. Journal of Statistical Computing and Simulation 16, 241–250.

See Also

Generalized Extreme Value Distribution, egevd, Hosking et al., 1985).

The Chi Distribution

Description

Density, distribution function, quantile function, and random generation for the chi distribution.

Usage

  dchi(x, df)
  pchi(q, df)
  qchi(p, df)
  rchi(n, df)

Arguments

Details

Elements of x, q, p, or df that are missing will cause the corresponding elements of the result to be missing.

The chi distribution with n degrees of freedom is the distribution of the positive square root of a random variable having a chi-squared distribution with n degrees of freedom.

The chi density function is given by:

f(x, \nu) = g(x^2, \nu) 2x, x > 0

where g(x,\nu) denotes the density function of a chi-square random variable with n degrees of freedom.

Value

density (dchi), probability (pchi), quantile (qchi), or random sample (rchi) for the chi distribution with df degrees of freedom.

Note

The chi distribution takes on positive real values. It is important because for a sample of n observations from a normal distribution, the sample standard deviation multiplied by the square root of the degrees of freedom \nu and divided by the true standard deviation follows a chi distribution with \nu degrees of freedom. The chi distribution is also used in computing exact prediction intervals for the next k observations from a normal distribution (see predIntNorm).

Author(s)

Steven P. Millard (EnvStats@ProbStatInfo.com)

References

Forbes, C., M. Evans, N. Hastings, and B. Peacock. (2011). Statistical Distributions. Fourth Edition. John Wiley and Sons, Hoboken, NJ.

Johnson, N. L., S. Kotz, and N. Balakrishnan. (1995). Continuous Univariate Distributions, Volume 1. Second Edition. John Wiley and Sons, New York.

See Also

Chisquare, Normal, predIntNorm, Probability Distributions and Random Numbers.

Examples

  # Density of a chi distribution with 4 degrees of freedom, evaluated at 3:

  dchi(3, 4) 
  #[1] 0.1499715

  #----------

  # The 95'th percentile of a chi distribution with 10 degrees of freedom:

  qchi(.95, 10) 
  #[1] 4.278672

  #----------

  # The cumulative distribution function of a chi distribution with 
  # 5 degrees of freedom evaluated at 3:

  pchi(3, 5) 
  #[1] 0.8909358

  #----------

  # A random sample of 2 numbers from a chi distribution with 7 degrees of freedom. 
  # (Note: the call to set.seed simply allows you to reproduce this example.)

  set.seed(20) 
  rchi(2, 7) 
  #[1] 3.271632 2.035179

Data Frame Summarizing Available Probability Distributions and Estimation Methods

Description

Data frame summarizing information about available probability distributions in R and the EnvStats package, and which distributions have associated functions for estimating distribution parameters.

Usage

Distribution.df

Format

A data frame with 35 rows corresponding to 35 different available probability distributions, and 25 columns containing information associated with these probability distributions.

Name

a character vector containing the name of the probability distribution (see the column labeled Name in the table below).

Type

a character vector indicating the type of distribution (see the column labeled Type in the table below). Possible values are "Finite Discrete", "Discrete", "Continuous", and "Mixed".

Support.Min

a character vector indicating the minimum value the random variable can assume (see the column labeled Range in the table below). The reason this is a character vector instead of a numeric vector is because some distributions have a lower bound that depends on the value of a distribution parameter. For example, the minimum value for a Uniform distribution is given by the value of the parameter min.

Support.Max

a character vector indicating the maximum value the random variable can assume (see the column labeled Range in the table below). The reason this is a character vector instead of a numeric vector is because some distributions have an upper bound that depends on the value of a distribution parameter. For example, the maximum value for a Uniform distribution is given by the value of the parameter max.

Estimation.Method(s)

a character vector indicating the names of the methods available to estimate the distribution parameter(s) (see the column labeled Estimation Method(s) in the table below). Possible values include "mle" (maximum likelihood), "mme" (method of moments), "mmue" (method of moments based on the unbiased estimate of variance), "mvue" (minimum variance unbiased), "qmle" (quasi-mle), etc., or some combination of these. In cases where an estimator is more than one kind, a slash (/) is used to denote all methods covered by the single estimator. For example, for the Binomial distribution, the sample proportion is the maximum likelihood, method of moments, and minimum variance unbiased estimator, so this method is denoted as "mle/mme/mvue". See the help files for the specific function listed under Estimating Distribution Parameters for an explanation of each of these estimation methods.

Quantile.Estimation.Method(s)

a character vector indicating the names of the methods available to estimate the distribution quantiles. For many distributions, these are the same as Estimation.Method(s). See the help files for the specific function listed under Estimating Distribution Quantiles for an explanation of each of these estimation methods.

Prediction.Interval.Method(s)

a character vector indicating the names of the methods available to create prediction intervals. See the help files for the specific function listed under Prediction Intervals for an explanation of each of these estimation methods.

Singly.Censored.Estimation.Method(s)

a character vector indicating the names of the methods available to estimate the distribution parameter(s) for Type I singly-censored data. See the help files for the specific function listed under Estimating Distribution Parameters in the help file for Censored Data for an explanation of each of these estimation methods.

Multiply.Censored.Estimation.Method(s)

a character vector indicating the names of the methods available to estimate the distribution parameter(s) for Type I multiply-censored data. See the help files for the specific function listed under Estimating Distribution Parameters in the help file for Censored Data for an explanation of each of these estimation methods.

Number.parameters

a numeric vector indicating the number of parameters associated with the distribution (see the column labeled Parameters in the table below).

Parameter.1

the columns labeled Parameter.1, Parameter.2, ..., Parameter.5 are character vectors containing the names of the distribution parameters (see the column labeled Parameters in the table below). If a distribution has n parameters and n < 5, then the columns labeled Parameter.n+1, ..., Parameter.5 are empty. For example, the Normal distribution has only two parameters associated with it (mean and sd), so the fields in Parameter.3, Parameter.4, and Parameter.5 are empty.

Parameter.2

see Parameter.1

Parameter.3

see Parameter.1

Parameter.4

see Parameter.1

Parameter.5

see Parameter.1

Parameter.1.Min

the columns labeled Parameter.1.Min, Parameter.2.Min, ...,
Parameter.5.Min are character vectors containing the minimum values that can be assumed by the distribution parameters (see the column labeled Parameter Range(s) in the table below).

The reason these are character vectors instead of numeric vectors is because some parameters have a lower bound of 0 but must be strictly bigger than 0 (e.g., the parameter sd for the Normal distribution), in which case the lower bound is .Machine$double.eps, which may vary from machine to machine. Also, some parameters have a lower bound that depends on the value of another parameter. For example, the parameter max for a Uniform distribution is bounded below by the value of the parameter min.

If a distribution has n parameters and n < 5, then the columns labeled Parameter.n+1.Min, ..., Parameter.5.Min have the missing value code (NA). For example, the Normal distribution has only two parameters associated with it (mean and sd) so the fields in
Parameter.3.Min, Parameter.4.Min, and Parameter.5.Min have NAs in them.

Parameter.2.Min

see Parameter.1.Min

Parameter.3.Min

see Parameter.1.Min

Parameter.4.Min

see Parameter.1.Min

Parameter.5.Min

see Parameter.1.Min

Parameter.1.Max

the columns labeled Parameter.1.Max, Parameter.2.Max, ...,
Parameter.5.Max are character vectors containing the maximum values that can be assumed by the distribution parameters (see the column labeled Parameter Range(s) in the table below).

The reason these are character vectors instead of numeric vectors is because some parameters have an upper bound that depends on the value of another parameter. For example, the parameter min for a Uniform distribution is bounded above by the value of the parameter max.

If a distribution has n parameters and n < 5, then the columns labeled Parameter.n+1.Max, ..., Parameter.5.Max have the missing value code (NA). For example, the Normal distribution has only two parameters associated with it (mean and sd) so the fields in
Parameter.3.Max, Parameter.4.Max, and Parameter.5.Max have NAs in them.

Parameter.2.Max

see Parameter.1.Max

Parameter.3.Max

see Parameter.1.Max

Parameter.4.Max

see Parameter.1.Max

Parameter.5.Max

see Parameter.1.Max

Details

The table below summarizes the probability distributions available in R and EnvStats. For each distribution, there are four associated functions for computing density values, percentiles, quantiles, and random numbers. The form of the names of these functions are dabb, pabb, qabb, and rabb, where abb is the abbreviated name of the distribution (see table below). These functions are described in the help file with the name of the distribution (see the first column of the table below). For example, the help file for Beta describes the behavior of dbeta, pbeta, qbeta, and rbeta.

For most distributions, there is also an associated function for estimating the distribution parameters, and the form of the names of these functions is eabb, where abb is the abbreviated name of the distribution (see table below). All of these functions are listed in the help file Estimating Distribution Parameters. For example, the function ebeta estimates the shape parameters of a Beta distribution based on a random sample of observations from this distribution.

For some distributions, there are functions to estimate distribution parameters based on Type I censored data. The form of the names of these functions is eabbSinglyCensored for singly censored data and eabbMultiplyCensored for multiply censored data. All of these functions are listed under the heading Estimating Distribution Parameters in the help file Censored Data.

Table 1a. Available Distributions: Name, Abbreviation, Type, and Range

Table 1b. Available Distributions: Name, Parameters, Parameter Default Values, Parameter Ranges, Estimation Method(s)

Source

The EnvStats package.

References

Millard, S.P. (2013). EnvStats: An R Package for Environmental Statistics. Springer, New York. https://link.springer.com/book/10.1007/978-1-4614-8456-1.

Concentrations in Exhibit 2 of 2002d USEPA Guidance Document

Description

Concentrations (mug/L) from an exposure unit.

Usage

data(EPA.02d.Ex.2.ug.per.L.vec)

Format

a numeric vector of concentrations (mug/L)

Source

USEPA. (2002d). Calculating Upper Confidence Limits for Exposure Point Concentrations at Hazardous Waste Sites. OSWER 9285.6-10, December 2002. Office of Emergency and Remedial Response, U.S. Environmental Protection Agency, Washington, D.C., p. 9.

Concentrations in Exhibit 4 of 2002d USEPA Guidance Document

Description

Concentrations (mg/kg) from an exposure unit.

Usage

data(EPA.02d.Ex.4.mg.per.kg.vec)

Format

a numeric vector of concentrations (mg/kg)

Source

USEPA. (2002d). Calculating Upper Confidence Limits for Exposure Point Concentrations at Hazardous Waste Sites. OSWER 9285.6-10, December 2002. Office of Emergency and Remedial Response, U.S. Environmental Protection Agency, Washington, D.C., p. 11.

Concentrations in Exhibit 6 of 2002d USEPA Guidance Document

Description

Concentrations (mg/kg) from an exposure unit.

Usage

data(EPA.02d.Ex.6.mg.per.kg.vec)

Format

a numeric vector of concentrations (mg/kg)

Source

USEPA. (2002d). Calculating Upper Confidence Limits for Exposure Point Concentrations at Hazardous Waste Sites. OSWER 9285.6-10, December 2002. Office of Emergency and Remedial Response, U.S. Environmental Protection Agency, Washington, D.C., p. 13.

Concentrations in Exhibit 9 of 2002d USEPA Guidance Document

Description

Concentrations (mg/L) from an exposure unit.

Usage

data(EPA.02d.Ex.9.mg.per.L.vec)

Format

a numeric vector of concentrations (mg/L)

Source

USEPA. (2002d). Calculating Upper Confidence Limits for Exposure Point Concentrations at Hazardous Waste Sites. OSWER 9285.6-10, December 2002. Office of Emergency and Remedial Response, U.S. Environmental Protection Agency, Washington, D.C., p. 16.

Nickel Concentrations from Example 10-1 of 2009 USEPA Guidance Document

Description

Nickel concentrations (ppb) from four wells (five observations per year for each well). The Guidance Document has the label “Year” instead of “Well”; corrected in Errata.

Usage

EPA.09.Ex.10.1.nickel.df

Format

A data frame with 20 observations on the following 3 variables.

Month

a numeric vector indicating the month the sample was taken

Well

a factor indicating the well number

Nickel.ppb

a numeric vector of nickel concentrations (ppb)

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery, Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C., p.10-12.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Arsenic Concentrations from Example 11-1 of 2009 USEPA Guidance Document

Description

Arsenic concentrations (ppb) at six wells (four observations per well).

Usage

EPA.09.Ex.11.1.arsenic.df

Format

A data frame with 24 observations on the following 3 variables.

Arsenic.ppb

a numeric vector of arsenic concentrations (ppb)

Month

a factor indicating the month of collection

Well

a factor indicating the well number

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.11-3.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Carbon Tetrachloride Concentrations from Example 12-1 of 2009 USEPA Guidance Document

Description

Carbon tetrachloride (CCL4) concentrations (ppb) at five background wells (four measures at each well).

Usage

EPA.09.Ex.12.1.ccl4.df

Format

A data frame with 20 observations on the following 2 variables.

Well

a factor indicating the well number

CCL4.ppb

a numeric vector of CCL4 concentrations (ppb)

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.12-3.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Naphthalene Concentrations from Example 12-4 of 2009 USEPA Guidance Document

Description

Naphthalene concentrations (ppb) at five background wells (five quarterly measures at each well).

Usage

EPA.09.Ex.12.4.naphthalene.df

Format

A data frame with 25 observations on the following 3 variables.

Quarter

a numeric vector indicating the quarter the sample was taken

Well

a factor indicating the well number

Naphthalene.ppb

a numeric vector of naphthalene concentrations (ppb)

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.12-12.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Iron Concentrations from Example 13-1 of 2009 USEPA Guidance Document

Description

Dissolved iron (Fe) concentrations (ppm) at six upgradient wells (four quarterly measures at each well).

Usage

EPA.09.Ex.13.1.iron.df

Format

A data frame with 24 observations on the following 4 variables.

Month

a numeric vector indicating the month the sample was taken

Year

a numeric vector indicating the year the sample was taken

Well

a factor indicating the well number

Iron.ppm

a numeric vector if iron concentrations (ppm)

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.13-3.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Manganese Concentrations from Example 14-1 of 2009 USEPA Guidance Document

Description

Manganese concentrations (ppm) at four background wells (eight quarterly measures at each well).

Usage

EPA.09.Ex.14.1.manganese.df

Format

A data frame with 32 observations on the following 3 variables.

Quarter

a numeric vector indicating the quarter the sample was taken

Well

a factor indicating the well number

Manganese.ppm

a numeric vector of manganese concentrations (ppm)

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.14-5.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Alkalinity Measures from Example 14-3 of 2009 USEPA Guidance Document

Description

Alkalinity measures (mg/L) collected from leachate at a solid waste landfill during a four and a half year period.

Usage

EPA.09.Ex.14.3.alkalinity.df

Format

A data frame with 54 observations on the following 2 variables.

Date

a Date object indicating the date of collection

Alkalinity.mg.per.L

a numeric vector of alkalinity measures (mg/L)

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.14-14.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Arsenic Concentrations from Example 14-4 of 2009 USEPA Guidance Document

Description

Sixteen quarterly measures of arsenic concentrations (ppb).

Usage

EPA.09.Ex.14.4.arsenic.df

Format

A data frame with 16 observations on the following 4 variables.

Sample.Date

a factor indicating the month and year of collection

Month

a factor indicating the month of collection

Year

a factor indicating the year of collection

Arsenic.ppb

a numeric vector of arsenic concentrations (ppb)

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.14-18.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Analyte Concentrations from Example 14-8 of 2009 USEPA Guidance Document

Description

Monthly unadjusted and adjusted analyte concentrations over a 3-year period. Adjusted concentrations are computed by subtracting the monthly mean and adding the overall mean.

Usage

EPA.09.Ex.14.8.df

Format

A data frame with 36 observations on the following 4 variables.

Month

a factor indicating the month of collection

Year

a numeric vector indicating the year of collection

Unadj.Conc

a numeric vector of unadjusted concentrations

Adj.Conc

a numeric vector adjusted concentrations

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.14-32.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Manganese Concentrations from Example 15-1 of 2009 USEPA Guidance Document

Description

Manganese concentrations (ppb) at five background wells (five measures at each well).

Usage

EPA.09.Ex.15.1.manganese.df

Format

A data frame with 25 observations on the following 5 variables.

Sample

a numeric vector indicating the sample number (1-5)

Well

a factor indicating the well number

Manganese.Orig.ppb

a character vector of the original manganese concentrations (ppb)

Manganese.ppb

a numeric vector of manganese concentrations with non-detects coded to their detecion limit

Censored

a logical vector indicating which observations are censored

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.15-10.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Sulfate Concentrations from Example 16-1 of 2009 USEPA Guidance Document

Description

Sulfate concentrations (ppm) at one background well and one downgradient well (eight quarterly measures at each well).

Usage

EPA.09.Ex.16.1.sulfate.df

Format

A data frame with 16 observations on the following 4 variables.

Month

a factor indicating the month of collection

Year

a factor indicating the year of collection

Well.type

a factor indicating the well type (background vs. downgradient)

Sulfate.ppm

a numeric vector of sulfate concentrations (ppm)

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.16-6.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Benzene Concentrations from Example 16-2 of 2009 USEPA Guidance Document

Description

Benzene concentrations (ppb) at one background and one downgradient well (eight monthly measures at each well).

Usage

EPA.09.Ex.16.2.benzene.df

Format

A data frame with 16 observations on the following 3 variables.

Month

a factor indicating the month of collection

Well.type

a factor indicating the well type (background vs. downgradient)

Benzene.ppb

a numeric vector of benzene concentrations (ppb)

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.16-9.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Copper Concentrations from Example 16-4 of 2009 USEPA Guidance Document

Description

Copper concentrations (ppb) at two background wells and one compliance well (six measures at each well).

Usage

EPA.09.Ex.16.4.copper.df

Format

A data frame with 18 observations on the following 4 variables.

Month

a factor indicating the month of collection

Well

a factor indicating the well number

Well.type

a factor indicating the well type (background vs. compliance)

Copper.ppb

a numeric vector of copper concentrations (ppb)

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.16-19.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Tetrachloroethylene Concentrations from Example 16-5 of 2009 USEPA Guidance Document

Description

Tetrachloroethylene (PCE) concentrations (ppb) at one background well and one compliance well.

Usage

EPA.09.Ex.16.5.PCE.df

Format

A data frame with 14 observations on the following 4 variables.

Well.type

a factor with levels Background Compliance

PCE.Orig.ppb

a character vector of original PCE concentrations (ppb)

PCE.ppb

a numeric vector of PCE concentrations (ppb) with nondetects set to their detection limit

Censored

a logical vector indicating which observations are censored

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.16-22.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Log-transformed Lead Concentrations from Example 17-1 of 2009 USEPA Guidance Document

Description

Log-transformed lead concentrations (ppb) at two background and four compliance wells (four quarterly measures at each well).

Usage

EPA.09.Ex.17.1.loglead.df

Format

A data frame with 24 observations on the following 4 variables.

Month

a factor indicating the month of collection; 1 = Jan, 2 = Apr, 3 = Jul, 4 = Oct

Well

a factor indicating the well number

Well.type

a factor indicating the well type (background vs. compliance)

LogLead

a numeric vector of log-transformed lead concentrations (ppb)

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.17-7.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Toluene Concentrations from Example 17-2 of 2009 USEPA Guidance Document

Description

Toluene concentrations (ppb) at two background and three compliance wells (five monthly measures at each well).

Usage

EPA.09.Ex.17.2.toluene.df

Format

A data frame with 25 observations on the following 6 variables.

Month

a factor indicating the month of collection

Well

a factor indicating the well number

Well.type

a factor indicating the well type (background vs. compliance)

Toluene.ppb.orig

a character vector of original toluene concentrations (ppb)

Toluene.ppb

a numeric vector of toluene concentrations (ppb) with nondetects set to their detection limit

Censored

a logical vector indicating which observations are censored

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.17-13.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Chrysene Concentrations from Example 17-3 of 2009 USEPA Guidance Document

Description

Chrysene concentrations (ppb) at two background and three compliance wells (four monthly measures at each well).

Usage

EPA.09.Ex.17.3.chrysene.df

Format

A data frame with 20 observations on the following 4 variables.

Month

a factor indicating the month of collection

Well

a factor indicating the well number

Well.type

a factor indicating the well type (background vs. compliance)

Chrysene.ppb

a numeric vector of chrysene concentrations (ppb)

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.17-17.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Log-transformed Chrysene Concentrations from Example 17-3 of 2009 USEPA Guidance Document

Description

Log-transformed chrysene concentrations (ppb) at two background and three compliance wells (four monthly measures at each well).

Usage

EPA.09.Ex.17.3.log.chrysene.df

Format

A data frame with 20 observations on the following 4 variables.

Month

a factor indicating the month of collection

Well

a factor indicating the well number

Well.type

a factor indicating the well type (background vs. compliance)

Log.Chrysene.ppb

a numeric vector of log-transformed chrysene concentrations (ppb)

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.17-18.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Copper Concentrations from Example 17-4 of 2009 USEPA Guidance Document

Description

Copper concentrations (ppb) at three background and two compliance wells (eight monthly measures at the background wells, four monthly measures at the compliance wells).

Usage

EPA.09.Ex.17.4.copper.df

Format

A data frame with 40 observations on the following 6 variables.

Month

a factor indicating the month of collection

Well

a factor indicating the well number

Well.type

a factor indicating the well type (background vs. compliance)

Copper.ppb.orig

a character vector of original copper concentrations (ppb)

Copper.ppb

a numeric vector of copper concentrations with nondetects set to their detection limit

Censored

a logical vector indicating which observations are censored

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.17-21.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Chloride Concentrations from Example 17-5 of 2009 USEPA Guidance Document

Description

Chloride concentrations (ppm) collected over a five-year period at a solid waste landfill.

Usage

EPA.09.Ex.17.5.chloride.df

Format

A data frame with 19 observations on the following 4 variables.

Date

a Date object indicating the date of collection

Chloride.ppm

a numeric vector of chloride concentrations (ppm)

Elapsed.Days

a numeric vector indicating the number of days since January 1, 2002

Residuals

a numeric vector of residuals from a linear regression trend fit

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.17-26.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Sulfate Concentrations from Example 17-6 of 2009 USEPA Guidance Document

Description

Sulfate concentrations (ppm) collected over several years. The date of collection is simply indicated by month and year of collection. The column Date is a Date object where the day of the month has been arbitrarily set to 1.

Usage

EPA.09.Ex.17.6.sulfate.df

Format

A data frame with 23 observations on the following 6 variables.

Sample.No

a numeric vector indicating the sample number

Year

a numeric vector indicating the year of collection

Month

a numeric vector indicating the month of collection

Sampling.Date

a numeric vector indicating the year and month of collection

Date

a Date object indicating the date of collection, where the day of the month is arbitrarily set to 1

Sulfate.ppm

a numeric vector of sulfate concentrations (ppm)

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.17-33.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Sodium Concentrations from Example 17-7 of 2009 USEPA Guidance Document

Description

Sodium concentrations (ppm) collected over several years. The sample dates are recorded as the year of collection (2-digit format) plus a fractional part indicating when during the year the sample was collected.

Usage

EPA.09.Ex.17.7.sodium.df

Format

A data frame with 10 observations on the following 2 variables.

Year

a numeric vector indicating the year of collection (a fractional number)

Sodium.ppm

a numeric vector of sodium concentrations (ppm)

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.17-36.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Arsenic Concentrations from Example 18-1 of 2009 USEPA Guidance Document

Description

Arsenic concentrations (ppb) in a single well at a solid waste landfill. Four observations per year over four years. Years 1-3 are the background period and Year 4 is the compliance period.

Usage

EPA.09.Ex.18.1.arsenic.df

Format

A data frame with 16 observations on the following 3 variables.

Year

a factor indicating the year of collection

Sampling.Period

a factor indicating the sampling period (background vs. compliance)

Arsenic.ppb

a numeric vector of arsenic concentrations (ppb)

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.18-10.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Chrysene Concentrations from Example 18-2 of 2009 USEPA Guidance Document

Description

Chrysene concentrations (ppb) at two background wells and one compliance well (four monthly measures at each well).

Usage

EPA.09.Ex.18.2.chrysene.df

Format

A data frame with 12 observations on the following 4 variables.

Month

a factor indicating the month of collection

Well

a factor indicating the well number

Well.type

a factor indicating the well type (background vs. compliance)

Chrysene.ppb

a numeric vector of chrysene concentrations (ppb)

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.18-15.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Trichloroethylene Concentrations from Example 18-3 of 2009 USEPA Guidance Document

Description

Trichloroethylene (TCE) concentrations (ppb) at three background wells and one compliance well. Six monthly measures at each background well, three monthly measures at the compliance well.

Usage

EPA.09.Ex.18.3.TCE.df

Format

A data frame with 24 observations on the following 6 variables.

Month

a factor indicating the month of collection

Well

a factor indicating the well number

Well.type

a factor indicating the well type (background vs. compliance)

TCE.ppb.orig

a character vector of original TCE concentrations (ppb)

TCE.ppb

a numeric vector of TCE concentrations (ppb) with nondetects set to their detection limit

Censored

a logical vector indicating which observations are censored

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.18-19.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Xylene Concentrations from Example 18-4 of 2009 USEPA Guidance Document

Description

Xylene concentrations (ppb) at three background wells and one compliance well. Eight monthly measures at each complaince well; three monthly measures at the compliance well.

Usage

EPA.09.Ex.18.4.xylene.df

Format

A data frame with 32 observations on the following 6 variables.

Month

a factor indicating the month of collection

Well

a factor indicating the well number

Well.type

a factor indicating the well type (background vs. compliance)

Xylene.ppb.orig

a character vector of original xylene concentrations (ppb)

Xylene.ppb

a numeric vector of xylene concentrations (ppb) with nondetects set to their detection limit

Censored

a logical vector indicating which observations are censored

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.18-22.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Sulfate Concentrations from Example 19-1 of 2009 USEPA Guidance Document

Description

Sulfate concentrations (mg/L) at four background wells.

Usage

EPA.09.Ex.19.1.sulfate.df

Format

A data frame with 25 observations on the following 7 variables.

Well

a factor indicating the well number

Month

a numeric vector indicating the month of collection

Day

a numeric vector indicating the day of the month of collection

Year

a numeric vector indicating the year of collection

Date

a Date object indicating the date of collection

Sulfate.mg.per.l

a numeric vector of sulfate concentrations (mg/L)

log.Sulfate.mg.per.l

a numeric vector of log-transformed sulfate concentrations (mg/L)

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.19-17.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Chloride Concentrations from Example 19-2 of 2009 USEPA Guidance Document

Description

Chloride concentrations (mg/L) at 10 compliance wells at a solid waste landfill. One year of quarterly measures at each well.

Usage

EPA.09.Ex.19.2.chloride.df

Format

A data frame with 40 observations on the following 2 variables.

Well

a factor indicating the well number

Chloride.mg.per.l

a numeric vector of chloride concentrations (mg/L)

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.19-19.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Mercury Concentrations from Example 19-5 of 2009 USEPA Guidance Document

Description

Mercury concentrations (ppb) at four background and two compliance wells.

Usage

EPA.09.Ex.19.5.mercury.df

Format

A data frame with 36 observations on the following 6 variables.

Event

a factor indicating the time of collection

Well

a factor indicating the well number

Well.type

a factor indicating the well type (background vs. compliance)

Mercury.ppb.orig

a character vector of original mercury concentrations (ppb)

Mercury.ppb

a numeric vector of mercury concentrations (ppb) with nondetects set to their detection limit

Censored

a logical vector indicating which observations are censored

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.19-33.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Nickel Concentrations from Example 20-1 of 2009 USEPA Guidance Document

Description

Nickel concentrations (ppb) at a single well. Eight monthly measures during the background period and eight monthly measures during the compliance period.

Usage

EPA.09.Ex.20.1.nickel.df

Format

A data frame with 16 observations on the following 4 variables.

Month

a factor indicating the month of collection

Year

a factor indicating the year of collection

Period

a factor indicating the period (baseline vs. compliance)

Nickel.ppb

a numeric vector of nickel concentrations (ppb)

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.20-4.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Aldicarb Concentrations from Example 21-1 of 2009 USEPA Guidance Document

Description

Aldicarb concentrations (ppb) at three compliance wells (four monthly measures at each well).

Usage

EPA.09.Ex.21.1.aldicarb.df

Format

A data frame with 12 observations on the following 3 variables.

Month

a factor indicating the month of collection

Well

a factor indicating the well number

Aldicarb.ppb

a numeric vector of aldicarb concentrations (ppb)

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.21-4.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Benzene Concentrations from Example 21-2 of 2009 USEPA Guidance Document

Description

Benzene concentrations (ppb) collected at a landfill that previously handled smelter waste and is now undergoing remediation efforts.

Usage

EPA.09.Ex.21.2.benzene.df

Format

A data frame with 8 observations on the following 4 variables.

Month

a numeric vector indicating the month of collection

Benzene.ppb.orig

a character vector of original benzene concentrations (ppb)

Benzene.ppb

a numeric vector of benzene concentrations (ppb) with nondetects set to their detection limit

Censored

a logical vector indicating which observations are censored

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.21-7.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Beryllium Concentrations from Example 21-5 of 2009 USEPA Guidance Document

Description

Beryllium concentrations (ppb) at one well (four years of quarterly measures).

Usage

data(EPA.09.Ex.21.5.beryllium.df)

Format

A data frame with 16 observations on the following 3 variables.

Year

a factor indicating the year of collection

Quarter

a factor indicating the quarter of collection

Beryllium.ppb

a numeric vector of beryllium concentrations (ppb)

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.21-18.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Nitrate Concentrations from Example 21-6 of 2009 USEPA Guidance Document

Description

Nitrate concentrations (mg/L) at a well used for drinking water.

Usage

EPA.09.Ex.21.6.nitrate.df

Format

A data frame with 12 observations on the following 5 variables.

Sampling.Date

a character vector indicating the sampling date

Date

a Date object indicating the sampling date

Nitrate.mg.per.l.orig

a character vector of original nitrate concentrations (mg/L)

Nitrate.mg.per.l

a numeric vector of nitrate concentrations (mg/L) with nondetects set to their detection limit

Censored

a logical vector indicating which observations are censored

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.21-22.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Trichloroethylene Concentrations from Example 21-7 of 2009 USEPA Guidance Document

Description

Trichloroethylene (TCE) concentrations (ppb) at a site undergoing remediation.

Usage

EPA.09.Ex.21.7.TCE.df

Format

A data frame with 10 observations on the following 2 variables.

Month

a numeric vector indicating the month of collection

TCE.ppb

a numeric vector of TCE concentrations (ppb)

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.21-26.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Vinyl Chloride Concentrations from Example 22-1 of 2009 USEPA Guidance Document

Description

Vinyl Chloride (VC) concentrations (ppb) during detection monitoring for two compliance wells. Four years of quarterly measures at each well. Compliance monitoring began with Year 2 of the sampling record.

Usage

EPA.09.Ex.22.1.VC.df

Format

A data frame with 32 observations on the following 5 variables.

Year

a factor indicating the year of collection

Quarter

a factor indicating the quarter of collection

Period

a factor indicating the period (background vs. compliance)

Well

a factor indicating the well number

VC.ppb

a numeric vector of VC concentrations (ppb)

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.22-6.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Specific Conductance from Example 22-2 of 2009 USEPA Guidance Document

Description

Specific conductance (\mumho) collected over several years at two wells at a hazardous waste facility.

Usage

EPA.09.Ex.22.2.Specific.Conductance.df

Format

A data frame with 43 observations on the following 3 variables.

Well

a factor indicating the well number

Date

a Date object indicating the date of collection

Specific.Conductance.umho

a numeric vector of specific conductance (\mumho)

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.22-11.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Sulfate Concentrations from Example 6-3 of 2009 USEPA Guidance Document

Description

Sulfate concentrations (ppm) at two background wells (five quarterly measures at each well).

Usage

EPA.09.Ex.6.3.sulfate.df

Format

A data frame with 10 observations on the following 4 variables.

Month

a numeric vector indicating the month the observations was taken

Year

a numeric vector indicating the year the observation was taken

Well

a factor indicating the well number

Sulfate.ppm

a numeric vector of sulfate concentrations (ppm)

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.6-20.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Arsenic concentrations from Example 7.1 of 2009 USEPA Guidance Document

Description

Arsenic concentrations (\mug/L) at a single well, consisting of: 8 historical observations, 4 future observations for Case 1, and 4 future observations for Case 2.

Usage

EPA.09.Ex.7.1.arsenic.df

Format

A data frame with 16 observations on the following 2 variables.

Data.Source

a factor with levels Historical, Case.1, Case.2

Arsenic.ug.per.l

a numeric vector of arsenic concentrations (\mug/L)

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.7-26.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Trichloroethene concentrations in Table 9.1 of 2009 USEPA Guidance Document

Description

Time series of trichloroethene (TCE) concentrations (mg/L) taken at 2 separate wells. Some observations are annotated with a data qualifier of U (nondetect) or J (estimated detected concentration).

Usage

EPA.09.Table.9.1.TCE.df

Format

A data frame with 30 observations on the following 5 variables.

Date.Collected

a factor indicating the date of collection

Date

a Date object indicating the date of collection

Well

a factor indicating the well number

TCE.mg.per.L

a numeric vector indicating the TCE concnetrations (mg/L)

Data.Qualifier

a factor indicating the data qualifier

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.9-3.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Arsenic, Mercury and Strontium Concentrations in Table 9-3 of 2009 USEPA Guidance Document

Description

Arsenic, mercury, and strontium concentrations (mg/L) from a single well collected approximately quarterly. Nondetects are indicated by the data qualifier U.

Usage

EPA.09.Table.9.3.df

Format

A data frame with 15 observations on the following 8 variables.

Date.Collected

a factor indicating the date of collection

Date

a Date object indicating the date of collection

Arsenic.mg.per.L

a numeric vector of arsenic concentrations (mg/L)

Arsenic.Data.Qualifier

a factor indicating the data qualifier for arsenic

Mercury.mg.per.L

a numeric vector of mercury concentrations (mg/L)

Mercury.Data.Qualifier

a factor indicating the data qualifier for mercury

Strontium.mg.per.L

a numeric vector of strontium concentrations

Strontium.Data.Qualifier

a factor indicating the data qualifier for strontium

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.9-13.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Nickel Concentrations in Table 9-4 of 2009 USEPA Guidance Document

Description

Nickel concentrations (ppb) from a single well.

Usage

EPA.09.Table.9.4.nickel.vec

Format

a numeric vector of nickel concentrations (ppb)

Source

USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Unified Guidance. EPA 530/R-09-007, March 2009. Office of Resource Conservation and Recovery Program Implementation and Information Division. U.S. Environmental Protection Agency, Washington, D.C. p.9-18.

USEPA. (2010). Errata Sheet - March 2009 Unified Guidance. EPA 530/R-09-007a, August 9, 2010. Office of Resource Conservation and Recovery, Program Information and Implementation Division. U.S. Environmental Protection Agency, Washington, D.C.

Aldicarb Concentrations from 1989 USEPA Guidance Document

Description

Aldicarb concentrations (ppb) at three compliance wells (four monthly samples at each well).

Usage

EPA.89b.aldicarb1.df

Format

A data frame with 12 observations on the following 3 variables.

Aldicarb

Aldicarb concentrations (ppb)

Month

a factor indicating the month of collection

Well

a factor indicating the well number

Source

USEPA. (1989b). Statistical Analysis of Ground-Water Monitoring Data at RCRA Facilities, Interim Final Guidance. EPA/530-SW-89-026. Office of Solid Waste, U.S. Environmental Protection Agency, Washington, D.C. p.6-4.

Aldicarb Concentrations from 1989 USEPA Guidance Document

Description

Aldicarb concentrations (ppm) at three compliance wells (four monthly samples at each well).

Usage

EPA.89b.aldicarb2.df

Format

A data frame with 12 observations on the following 3 variables.

Aldicarb

Aldicarb concentrations (ppm)

Month

a factor indicating the month of collection

Well

a factor indicating the well number

Source

USEPA. (1989b). Statistical Analysis of Ground-Water Monitoring Data at RCRA Facilities, Interim Final Guidance. EPA/530-SW-89-026. Office of Solid Waste, U.S. Environmental Protection Agency, Washington, D.C. p.6-13.

Benzene Concentrations from 1989 USEPA Guidance Document

Description

Benzene concentrations (ppm) at one background and five compliance wells (four monthly samples for each well).

Usage

EPA.89b.benzene.df

Format

A data frame with 24 observations on the following 6 variables.

Benzene.orig

a character vector of the original observations

Benzene

a numeric vector with <1 observations coded as 1

Censored

a logical vector indicating which observations are censored

Month

a factor indicating the month of collection

Well

a factor indicating the well number

Well.type

a factor indicating the well type (background vs. compliance)

Source

USEPA. (1989b). Statistical Analysis of Ground-Water Monitoring Data at RCRA Facilities, Interim Final Guidance. EPA/530-SW-89-026. Office of Solid Waste, U.S. Environmental Protection Agency, Washington, D.C. p.5-18.

Cadmium Concentrations from 1989 USEPA Guidance Document

Description

Cadmium concentrations (mg/L) at one set of background and one set of compliance wells. Nondetects reported as "BDL". Detection limit not given.

Usage

EPA.89b.cadmium.df

Format

A data frame with 88 observations on the following 4 variables.

Cadmium.orig

a character vector of the original cadmium observations (mg/L)

Cadmium

a numeric vector with BDL coded as 0

Censored

a logical vector indicating which observations are censored

Well.type

a factor indicating the well type (background vs. compliance)

Source

USEPA. (1989b). Statistical Analysis of Ground-Water Monitoring Data at RCRA Facilities, Interim Final Guidance. EPA/530-SW-89-026. Office of Solid Waste, U.S. Environmental Protection Agency, Washington, D.C. p.8-6.

Chlordane Concentrations from 1989 USEPA Guidance Document

Description

Chlordane concentrations (ppm) in 24 water samples. Two possible phases: dissolved (18 observations) and immiscible (6 observations).

Usage

EPA.89b.chlordane1.df

Format

A data frame with 24 observations on the following 2 variables.

Chlordane

Chlordane concentrations (ppm)

Phase

a factor indicating the phase (dissolved vs. immiscible)

Source

USEPA. (1989b). Statistical Analysis of Ground-Water Monitoring Data at RCRA Facilities, Interim Final Guidance. EPA/530-SW-89-026. Office of Solid Waste, U.S. Environmental Protection Agency, Washington, D.C. p.4-8.

Chlordane Concentrations from 1989 USEPA Guidance Document

Description

Chlordane concentrations (ppb) at one background and one compliance well. Observations taken during four separate months over two years. Four replicates taken for each “month/year/well type” combination.

Usage

data(EPA.89b.chlordane2.df)

Format

A data frame with 32 observations on the following 5 variables.

Chlordane

Chlordane concentration (ppb)

Month

a factor indicating the month of collection

Year

a numeric vector indicating the year of collection (85 or 86)

Replicate

a factor indicating the replicate number

Well.type

a factor indicating the well type (background vs. compliance)

Source

USEPA. (1989b). Statistical Analysis of Ground-Water Monitoring Data at RCRA Facilities, Interim Final Guidance. EPA/530-SW-89-026. Office of Solid Waste, U.S. Environmental Protection Agency, Washington, D.C. p.5-27.

EDB Concentrations from 1989 USEPA Guidance Document

Description

EDB concentrations (ppb) at three compliance wells (four monthly samples at each well).

Usage

EPA.89b.edb.df

Format

A data frame with 12 observations on the following 3 variables.

EDB

EDB concentrations (ppb)

Month

a factor indicating the month of collection

Well

a factor indicating the well number

Source

USEPA. (1989b). Statistical Analysis of Ground-Water Monitoring Data at RCRA Facilities, Interim Final Guidance. EPA/530-SW-89-026. Office of Solid Waste, U.S. Environmental Protection Agency, Washington, D.C. p.6-6.

Lead Concentrations from 1989 USEPA Guidance Document

Description

Lead concentrations (ppm) at two background and four compliance wells (four monthly samples for each well).

Usage

EPA.89b.lead.df

Format

A data frame with 24 observations on the following 4 variables.

Lead

Lead concentrations (ppm)

Month

a factor indicating the month of collection

Well

a factor indicating the well number

Well.type

a factor indicating the well type (background vs. compliance)

Source

USEPA. (1989b). Statistical Analysis of Ground-Water Monitoring Data at RCRA Facilities, Interim Final Guidance. EPA/530-SW-89-026. Office of Solid Waste, U.S. Environmental Protection Agency, Washington, D.C. p.5-23.

Log-transformed Lead Concentrations from 1989 USEPA Guidance Document

Description

Log-transformed lead concentrations (\mug/L) at two background and four compliance wells (four monthly samples for each well).

Usage

EPA.89b.loglead.df

Format

A data frame with 24 observations on the following 4 variables.

LogLead

Natural logarithm of lead concentrations (\mug/L)

Month

a factor indicating the month of collection

Well

a factor indicating the well number

Well.type

a factor indicating the well type (background vs. compliance)

Source

USEPA. (1989b). Statistical Analysis of Ground-Water Monitoring Data at RCRA Facilities, Interim Final Guidance. EPA/530-SW-89-026. Office of Solid Waste, U.S. Environmental Protection Agency, Washington, D.C. p.5-11.

Manganese Concentrations from 1989 USEPA Guidance Document

Description

Manganese concentrations at six monitoring wells (four monthly samples for each well).

Usage

EPA.89b.manganese.df

Format

A data frame with 24 observations on the following 3 variables.

Manganese

Manganese concentrations

Month

a factor indicating the month of collection

Well

a factor indicating the well number

Source

USEPA. (1989b). Statistical Analysis of Ground-Water Monitoring Data at RCRA Facilities, Interim Final Guidance. EPA/530-SW-89-026. Office of Solid Waste, U.S. Environmental Protection Agency, Washington, D.C. p.4-19.

Sulfate Concentrations from 1989 USEPA Guidance Document

Description

Sulfate concentrations (mg/L). Nondetects reported as <1450.

Usage

data(EPA.89b.sulfate.df)

Format

A data frame with 24 observations on the following 3 variables.

Sulfate.orig

a character vector of original sulfate concentration (mg/L)

Sulfate

a numeric vector of sulfate concentations with <1450 coded as 1450

Censored

a logical vector indicating which observations are censored

Source

USEPA. (1989b). Statistical Analysis of Ground-Water Monitoring Data at RCRA Facilities, Interim Final Guidance. EPA/530-SW-89-026. Office of Solid Waste, U.S. Environmental Protection Agency, Washington, D.C. p.8-9.

T-29 Concentrations from 1989 USEPA Guidance Document

Description

T-29 concentrations (ppm) at two compliance wells (four monthly samples at each well, four replicates within each month). Detection limit is not given.

Usage

EPA.89b.t29.df

Format

A data frame with 32 observations on the following 6 variables.

T29.orig

a character vector of the original T-29 concentrations (ppm)

T29

a numeric vector of T-29 concentrations with <? coded as 0

Censored

a logical vector indicating which observations are censored

Month

a factor indicating the month of collection

Replicate

a factor indicating the replicate number

Well

a factor indicating the well number

Source

USEPA. (1989b). Statistical Analysis of Ground-Water Monitoring Data at RCRA Facilities, Interim Final Guidance. EPA/530-SW-89-026. Office of Solid Waste, U.S. Environmental Protection Agency, Washington, D.C. p.6-10.

Total Organic Carbon Concentrations from 1989 USEPA Guidance Document

Description

Numeric vector containing total organic carbon (TOC) concentrations (mg/L).

Usage

EPA.89b.toc.vec

Format

A numeric vector with 19 elements containing TOC concentrations (mg/L).

Source

USEPA. (1989b). Statistical Analysis of Ground-Water Monitoring Data at RCRA Facilities, Interim Final Guidance. EPA/530-SW-89-026. Office of Solid Waste, U.S. Environmental Protection Agency, Washington, D.C. p.8-13.

Arsenic Concentrations from 1992 USEPA Guidance Document

Description

Arsenic concentrations (ppm) at six monitoring wells (four monthly samples for each well).

Usage

EPA.92c.arsenic1.df

Format

A data frame with 24 observations on the following 3 variables.

Arsenic

Arsenic concentrations (ppm)

Month

a factor indicating the month of collection

Well

a factor indicating the well number

Source

USEPA. (1992c). Statistical Analysis of Ground-Water Monitoring Data at RCRA Facilities: Addendum to Interim Final Guidance. Office of Solid Waste, U.S. Environmental Protection Agency, Washington, D.C. p.21.

Arsenic Concentrations from 1992 USEPA Guidance Document

Description

Arsenic concentrations (ppb) at three background wells and one compliance well (six monthly samples for each well; first four missing at compliance well). Nondetects reported as <5.

Usage

EPA.92c.arsenic2.df

Format

A data frame with 24 observations on the following 6 variables.

Arsenic.orig

a character vector of original arsenic concentrations (ppb)

Arsenic

a numeric vector of arsenic concentrations with <5 coded as 5

Censored

a logical vector indicating which observations are censored

Month

a factor indicating the month of collection

Well

a factor indicating the well number

Well.type

a factor indicating the well type (background vs. compliance)

Source

USEPA. (1992c). Statistical Analysis of Ground-Water Monitoring Data at RCRA Facilities: Addendum to Interim Final Guidance. Office of Solid Waste, U.S. Environmental Protection Agency, Washington, D.C. p.60.

Arsenic Concentrations from 1992 USEPA Guidance Document

Description

Arsenic concentrations at one background and one compliance monitoring well. Three years of observations for background well, two years of observations for compliance well, four samples per year for each well.

Usage

EPA.92c.arsenic3.df

Format

A data frame with 20 observations on the following 3 variables.

Arsenic

a numeric vector of arsenic concentrations

Year

a factor indicating the year of collection

Well.type

a factor indicating the well type (background vs. compliance)

Source

USEPA. (1992c). Statistical Analysis of Ground-Water Monitoring Data at RCRA Facilities: Addendum to Interim Final Guidance. Office of Solid Waste, U.S. Environmental Protection Agency, Washington, D.C.

Benzene Concentrations from 1992 USEPA Guidance Document

Description

Benzene concentrations (ppb) at six background wells (six monthly samples for each well). Nondetects reported as <2.

Usage

EPA.92c.benzene1.df

Format

A data frame with 36 observations on the following 5 variables.

Benzene.orig

a character vector of original benzene concentrations (ppb)

Benzene

a numeric vector of benzene concentrations with <2 coded as 2

Censored

a logical vector indicating which observations are censored

Month

a factor indicating the month of collection

Well

a factor indicating the well number

Source

USEPA. (1992c). Statistical Analysis of Ground-Water Monitoring Data at RCRA Facilities: Addendum to Interim Final Guidance. Office of Solid Waste, U.S. Environmental Protection Agency, Washington, D.C. p.36.

Benzene Concentrations from 1992 USEPA Guidance Document

Description

Benzene concentrations (ppb) at one background and one compliance well. Four observations per month for each well. Background well sampled in months 1,2, and 3; compliance well sampled in months 4 and 5.

Usage

EPA.92c.benzene2.df

Format

A data frame with 20 observations on the following 3 variables.

Benzene

a numeric vector of benzene concentrations (ppb)

Month

a factor indicating the month of collection

Well.type

a factor indicating the well type (background vs. compliance)

Source

USEPA. (1992c). Statistical Analysis of Ground-Water Monitoring Data at RCRA Facilities: Addendum to Interim Final Guidance. Office of Solid Waste, U.S. Environmental Protection Agency, Washington, D.C. p.56.

Carbon Tetrachloride Concentrations from 1992 USEPA Guidance Document

Description

Carbon tetrachloride (CCL4) concentrations (ppb) at five wells (four monthly samples at each well).

Usage

EPA.92c.ccl4.df

Format

A data frame with 20 observations on the following 3 variables.

CCL4

a numeric vector of carbon tetrachloride concentrations (ppb)

Month

a factor indicating the month of collection

Well

a factor indicating the well number

Source

USEPA. (1992c). Statistical Analysis of Ground-Water Monitoring Data at RCRA Facilities: Addendum to Interim Final Guidance. Office of Solid Waste, U.S. Environmental Protection Agency, Washington, D.C. p.80.

Chrysene Concentrations from 1992 USEPA Guidance Document

Description

Chrysene concentrations (ppb) at five compliance wells (four monthly samples for each well).

Usage

EPA.92c.chrysene.df

Format

A data frame with 20 observations on the following 3 variables.

Chrysene

a numeric vector of chrysene concentrations (ppb)

Month

a factor indicating the month of collection

Well

a factor indicating the well number

Source

USEPA. (1992c). Statistical Analysis of Ground-Water Monitoring Data at RCRA Facilities: Addendum to Interim Final Guidance. Office of Solid Waste, U.S. Environmental Protection Agency, Washington, D.C. p.52.

Copper Concentrations from 1992 USEPA Guidance Document

Description

Copper concentrations (ppb) at two background and one compliance wells (six monthly samples for each well).

Usage

EPA.92c.copper1.df

Format

A data frame with 18 observations on the following 4 variables.

Copper

a numeric vector of copper concentrations (ppb)

Month

a factor indicating the month of collection

Well

a factor indicating the well number

Well.type

a factor indicating the well type (background vs. compliance)

Source

USEPA. (1992c). Statistical Analysis of Ground-Water Monitoring Data at RCRA Facilities: Addendum to Interim Final Guidance. Office of Solid Waste, U.S. Environmental Protection Agency, Washington, D.C. p.47.

Copper Concentrations from 1992 USEPA Guidance Document

Description

Copper concentrations (ppb) at three background and two compliance wells (eight monthly samples for each well; first four missing at compliance wells). Nondetects reported as <5.

Usage

EPA.92c.copper2.df

Format

A data frame with 40 observations on the following 6 variables.

Copper.orig

a character vector of original copper concentrations (ppb)

Copper

a numeric vector of copper concentrations with <5 coded as 5

Censored

a logical vector indicating which observations are censored

Month

a factor indicating the month of collection

Well

a factor indicating the well number

Well.type

a factor indicating the well type (background vs. compliance)

Source

USEPA. (1992c). Statistical Analysis of Ground-Water Monitoring Data at RCRA Facilities: Addendum to Interim Final Guidance. Office of Solid Waste, U.S. Environmental Protection Agency, Washington, D.C. p.55.

Log-transformed Nickel Concentrations from 1992 USEPA Guidance Document

Description

Log-transformed nickel concentrations (ppb) at four monitoring wells (five monthly samples for each well).

Usage

EPA.92c.lognickel1.df

Format

A data frame with 20 observations on the following 3 variables.

LogNickel

a numeric vector of log-transformed nickel concentrations (ppb)

Month

a factor indicating the month of collection

Well

a factor indicating the well number

Source

USEPA. (1992c). Statistical Analysis of Ground-Water Monitoring Data at RCRA Facilities: Addendum to Interim Final Guidance. Office of Solid Waste, U.S. Environmental Protection Agency, Washington, D.C. p.15.

Nickel Concentrations from 1992 USEPA Guidance Document

Description

Nickel concentrations (ppb) at four monitoring wells (five monthly samples for each well).

Usage

EPA.92c.nickel1.df

Format

A data frame with 20 observations on the following 3 variables.

Nickel

a numeric vector of nickel concentrations (ppb)

Month

a factor indicating the month of collection

Well

a factor indicating the well number

Source

USEPA. (1992c). Statistical Analysis of Ground-Water Monitoring Data at RCRA Facilities: Addendum to Interim Final Guidance. Office of Solid Waste, U.S. Environmental Protection Agency, Washington, D.C. p.7.

Nickel Concentrations from 1992 USEPA Guidance Document

Description

Nickel concentrations (ppb) at a monitoring well (eight months of samples, two samples for each sampling occasion).

Usage

EPA.92c.nickel2.df

Format

A data frame with 16 observations on the following 3 variables.

Nickel

a numeric vector of nickel concentrations (ppb)

Month

a factor indicating the month of collection

Sample

a factor indicating the sample (replicate) number

Source

USEPA. (1992c). Statistical Analysis of Ground-Water Monitoring Data at RCRA Facilities: Addendum to Interim Final Guidance. Office of Solid Waste, U.S. Environmental Protection Agency, Washington, D.C. p.78.

Toluene Concentrations from 1992 USEPA Guidance Document

Description

Toluene concentrations (ppb) at two background and three compliance wells (five monthly samples at each well). Nondetects reported as <5.

Usage

EPA.92c.toluene.df

Format

A data frame with 25 observations on the following 6 variables.

Toluene.orig

a character vector of original toluene concentrations (ppb)

Toluene

a numeric vector of toluene concentrations with <5 coded as 5

Censored

a logical vector indicating which observations are censored

Month

a factor indicating the month of collection

Well

a factor indicating the well number

Well.type

a factor indicating the well type (background vs. compliance)

Source

USEPA. (1992c). Statistical Analysis of Ground-Water Monitoring Data at RCRA Facilities: Addendum to Interim Final Guidance. Office of Solid Waste, U.S. Environmental Protection Agency, Washington, D.C. p.43.

Zinc Concentrations from 1992 USEPA Guidance Document

Description

Zinc concentrations (ppb) at five background wells (eight samples for each well). Nondetects reported as <7.

Usage

EPA.92c.zinc.df

Format

A data frame with 40 observations on the following 5 variables.

Zinc.orig

a character vector of original zinc concentrations (ppb)

Zinc

a numeric vector of zinc concentrations with <7 coded as 7

Censored

a logical vector indicating which observations are censored

Sample

a factor indicating the sample number

Well

a factor indicating the well number

Source

USEPA. (1992c). Statistical Analysis of Ground-Water Monitoring Data at RCRA Facilities: Addendum to Interim Final Guidance. Office of Solid Waste, U.S. Environmental Protection Agency, Washington, D.C. p.30.

Chromium Concentrations from 1992 USEPA Guidance Document

Description

Chromium concentrations (mg/kg) in soil samples collected randomly over a Superfund site.

Usage

EPA.92d.chromium.df

Format

A data frame with 15 observations on the following variable.

Cr

a numeric vector of chromium concentrations (mg/kg)

Source

USEPA. (1992d). Supplemental Guidance to RAGS: Calculating the Concentration Term. Publication 9285.7-081, May 1992. Intermittent Bulletin, Volume 1, Number 1. Office of Emergency and Remedial Response, Hazardous Site Evaluation Division, OS-230. Office of Solid Waste and Emergency Response, U.S. Environmental Protection Agency, Washington, D.C.

Chromium Concentrations from 1992 USEPA Guidance Document

Description

Chromium concentrations (mg/kg) in soil samples collected randomly over a Superfund site.

Usage

EPA.92d.chromium.vec

Format

A numeric vector with 15 observations.

Source

USEPA. (1992d). Supplemental Guidance to RAGS: Calculating the Concentration Term. Publication 9285.7-081, May 1992. Intermittent Bulletin, Volume 1, Number 1. Office of Emergency and Remedial Response, Hazardous Site Evaluation Division, OS-230. Office of Solid Waste and Emergency Response, U.S. Environmental Protection Agency, Washington, D.C.

Lead Concentrations from 1994 USEPA Guidance Document

Description

Lead concentrations (mg/Kg) in soil samples at a reference area and a cleanup area. Nondetects reported as <39. There are 14 observations for each area.

Usage

EPA.94b.lead.df

Format

A data frame with 28 observations on the following 4 variables.

Lead.orig

a character vector of original lead concentrations (mg/Kg)

Lead

a numeric vector of lead concentrations with <39 coded as 39

Censored

a logical vector indicating which observations are censored

Area

a factor indicating the area (cleanup vs. reference)

Source

USEPA. (1994b). Statistical Methods for Evaluating the Attainment of Cleanup Standards, Volume 3: Reference-Based Standards for Soils and Solid Media. EPA/230-R-94-004. Office of Policy, Planning, and Evaluation, U.S. Environmental Protection Agency, Washington, D.C. pp.6.20–6.21.

1,2,3,4-Tetrachlorobenzene Concentrations from 1994 USEPA Guidance Document

Description

1,2,3,4-Tetrachlorobenzene (TcCB) concentrations (ppb) in soil samples at a reference area and a cleanup area. There are 47 observations for the reference area and 77 for the cleanup area. There is only one nondetect in the dataset (it's in the cleanup area), and it is reported as ND. Here it is assumed the nondetect is less than the smallest reported value, which is 0.09 ppb. Note that on page 6.23 of USEPA (1994b), a value of 25.5 for the Cleanup Unit was erroneously omitted.

Usage

EPA.94b.tccb.df

Format

A data frame with 124 observations on the following 4 variables.

TcCB.orig

a character vector with the original tetrachlorobenzene concentrations (ppb)

TcCB

a numeric vector of tetrachlorobenzene with <0.99 coded as 0.99

Censored

a logical vector indicating which observations are censored

Area

a factor indicating the area (cleanup vs. reference)

Source

USEPA. (1994b). Statistical Methods for Evaluating the Attainment of Cleanup Standards, Volume 3: Reference-Based Standards for Soils and Solid Media. EPA/230-R-94-004. Office of Policy, Planning, and Evaluation, U.S. Environmental Protection Agency, Washington, D.C. pp.6.22-6.25.

Calibration Data for Cadmium at Mass 111

Description

Calibration data for cadmium at mass 111 (ng/L; method 1638 ICPMS) that appeared in Gibbons et al. (1997b) and were provided to them by the U.S. EPA.

Usage

EPA.97.cadmium.111.df

Format

A data frame with 35 observations on the following 2 variables.

Cadmium

Observed concentation of cadmium (ng/L)

Spike

“True” concentration of cadmium taken from a standard (ng/L)

Source

Gibbons, R.D., D.E. Coleman, and R.F. Maddalone. (1997b). Response to Comment on "An Alternative Minimum Level Definition for Analytical Quantification". Environmental Science and Technology, 31(12), 3729–3731.

The Extreme Value (Gumbel) Distribution

Description

Density, distribution function, quantile function, and random generation for the (largest) extreme value distribution.

Usage

  devd(x, location = 0, scale = 1)
  pevd(q, location = 0, scale = 1)
  qevd(p, location = 0, scale = 1)
  revd(n, location = 0, scale = 1)

Arguments

Details

Let X be an extreme value random variable with parameters location=\eta and scale=\theta. The density function of X is given by:

f(x; \eta, \theta) = \frac{1}{\theta} e^{-(x-\eta)/\theta} exp[-e^{-(x-\eta)/\theta}]

where -\infty < x, \eta < \infty and \theta > 0.

The cumulative distribution function of X is given by:

F(x; \eta, \theta) = exp[-e^{-(x-\eta)/\theta}]

The p^{th} quantile of X is given by:

x_{p} = \eta - \theta log[-log(p)]

The mode, mean, variance, skew, and kurtosis of X are given by:

Mode(X) = \eta

E(X) = \eta + \epsilon \theta

Var(X) = \theta^2 \pi^2 / 6

Skew(X) = \sqrt{\beta_1} = 1.139547

Kurtosis(X) = \beta_2 = 5.4

where \epsilon denotes Euler's constant, which is equivalent to -digamma(1).

Value

density (devd), probability (pevd), quantile (qevd), or random sample (revd) for the extreme value distribution with location parameter(s) determined by location and scale parameter(s) determined by scale.

Note

There are three families of extreme value distributions. The one described here is the Type I, also called the Gumbel extreme value distribution or simply Gumbel distribution. The name “extreme value” comes from the fact that this distribution is the limiting distribution (as n approaches infinity) of the greatest value among n independent random variables each having the same continuous distribution.

The Gumbel extreme value distribution is related to the exponential distribution as follows. Let Y be an exponential random variable with parameter rate=\lambda. Then X = \eta - log(Y) has an extreme value distribution with parameters location=\eta and scale=1/\lambda.

The distribution described above and used by devd, pevd, qevd, and revd is the largest extreme value distribution. The smallest extreme value distribution is the limiting distribution (as n approaches infinity) of the smallest value among n independent random variables each having the same continuous distribution. If X has a largest extreme value distribution with parameters
location=\eta and scale=\theta, then Y = -X has a smallest extreme value distribution with parameters location=-\eta and scale=\theta. The smallest extreme value distribution is related to the Weibull distribution as follows. Let Y be a Weibull random variable with parameters shape=\beta and scale=\alpha. Then X = log(Y) has a smallest extreme value distribution with parameters location=log(\alpha) and scale=1/\beta.

The extreme value distribution has been used extensively to model the distribution of streamflow, flooding, rainfall, temperature, wind speed, and other meteorological variables, as well as material strength and life data.

Author(s)

Steven P. Millard (EnvStats@ProbStatInfo.com)

References

Forbes, C., M. Evans, N. Hastings, and B. Peacock. (2011). Statistical Distributions. Fourth Edition. John Wiley and Sons, Hoboken, NJ.

Johnson, N. L., S. Kotz, and N. Balakrishnan. (1995). Continuous Univariate Distributions, Volume 2. Second Edition. John Wiley and Sons, New York.

See Also

eevd, GEVD, Probability Distributions and Random Numbers.

Examples

  # Density of an extreme value distribution with location=0, scale=1, 
  # evaluated at 0.5:

  devd(.5) 
  #[1] 0.3307043

  #----------

  # The cdf of an extreme value distribution with location=1, scale=2, 
  # evaluated at 0.5:

  pevd(.5, 1, 2) 
  #[1] 0.2769203

  #----------

  # The 25'th percentile of an extreme value distribution with 
  # location=-2, scale=0.5:

  qevd(.25, -2, 0.5) 
  #[1] -2.163317

  #----------

  # Random sample of 4 observations from an extreme value distribution with 
  # location=5, scale=2. 
  # (Note: the call to set.seed simply allows you to reproduce this example.)

  set.seed(20) 
  revd(4, 5, 2) 
  #[1] 9.070406 7.669139 4.511481 5.903675

The Empirical Distribution Based on a Set of Observations

Description

Density, distribution function, quantile function, and random generation for the empirical distribution based on a set of observations

Usage

  demp(x, obs, discrete = FALSE, density.arg.list = NULL)
  pemp(q, obs, discrete = FALSE, 
    prob.method = ifelse(discrete, "emp.probs", "plot.pos"), 
    plot.pos.con = 0.375) 
  qemp(p, obs, discrete = FALSE, 
    prob.method = ifelse(discrete, "emp.probs", "plot.pos"), 
    plot.pos.con = 0.375)
  remp(n, obs)

Arguments

Details

Let x_1, x_2, \ldots, x_n denote a random sample of n observations from some unknown probability distribution (i.e., the elements of the argument obs), and let x_{(i)} denote the i^{th} order statistic, that is, the i^{th} largest observation, for i = 1, 2, \ldots, n.

Estimating Density
The function demp computes the empirical probability density function. If the observations are assumed to come from a discrete distribution, the probability density (mass) function is estimated by:

\hat{f}(x) = \widehat{Pr}(X = x) = \frac{\sum^n_{i=1} I_{[x]}(x_i)}{n}

where I is the indicator function:

That is, the estimated probability of observing the value x is simply the observed proportion of observations equal to x.

If the observations are assumed to come from a continuous distribution, the function demp calls the R function density to compute the estimated density based on the values specified in the argument obs, and then uses linear interpolation to estimate the density at the values specified in the argument x. See the R help file for density for more information on how the empirical density is computed in the continuous case.

Estimating Probabilities
The function pemp computes the estimated cumulative distribution function (cdf), also called the empirical cdf (ecdf). If the observations are assumed to come from a discrete distribution, the value of the cdf evaluated at the i^{th} order statistic is usually estimated by:

\hat{F}[x_{(i)}] = \widehat{Pr}(X \le x_{(i)}) = \hat{p}_i = \frac{\sum^n_{j=1} I_{(-\infty, x_{(i)}]}(x_j)}{n}

where:

(D'Agostino, 1986a). That is, the estimated value of the cdf at the i^{th} order statistic is simply the observed proportion of observations less than or equal to the i^{th} order statistic. This estimator is sometimes called the “empirical probabilities” estimator and is intuitively appealing. The function pemp uses the above equations to compute the empirical cdf when prob.method="emp.probs".

For any general value of x, when the observations are assumed to come from a discrete distribution, the value of the cdf is estimated by:

The function pemp uses the above equation when discrete=TRUE.

If the observations are assumed to come from a continuous distribution, the value of the cdf evaluated at the i^{th} order statistic is usually estimated by:

\hat{F}[x_{(i)}] = \hat{p}_i = \frac{i - a}{n - 2a + 1}

where a denotes the plotting position constant and 0 \le a \le 1 (Cleveland, 1993, p.18; D'Agostino, 1986a, pp.8,25). The estimators defined by the above equation are called plotting positions and are used to construct probability plots. The function pemp uses the above equation when
prob.method="plot.pos".

For any general value of x, the value of the cdf is estimated by linear interpolation:

where

r = \frac{x - x_{(i)}}{x_{(i+1)} - x_{(i)}}

(Chambers et al., 1983). The function pemp uses the above two equations when discrete=FALSE.

Estimating Quantiles
The function qemp computes the estimated quantiles based on the observed data. If the observations are assumed to come from a discrete distribution, the p^{th} quantile is usually estimated by:

The function qemp uses the above equation when discrete=TRUE.

If the observations are assumed to come from a continuous distribution, the p^{th} quantile is usually estimated by linear interpolation:

where

r = \frac{p - \hat{p}_{i-1}}{\hat{p}_i - \hat{p}_{i-1}}

The function qemp uses the above two equations when discrete=FALSE.

Generating Random Numbers From the Empirical Distribution
The function remp simply calls the R function sample to sample the elements of obs with replacement.

Value

density (demp), probability (pemp), quantile (qemp), or random sample (remp) for the empirical distribution based on the data contained in the vector obs.

Note

The function demp let's you perform nonparametric density estimation. The function pemp computes the value of the empirical cumulative distribution function (ecdf) for user-specified quantiles. The ecdf is a nonparametric estimate of the true cdf (see ecdfPlot). The function qemp computes nonparametric estimates of quantiles (see the help files for eqnpar and quantile). The function remp let's you sample a set of observations with replacement, which is often done while bootstrapping or performing some other kind of Monte Carlo simulation.

Author(s)

Steven P. Millard (EnvStats@ProbStatInfo.com)

References

Chambers, J.M., W.S. Cleveland, B. Kleiner, and P.A. Tukey. (1983). Graphical Methods for Data Analysis. Duxbury Press, Boston, MA, pp.11–16.

Cleveland, W.S. (1993). Visualizing Data. Hobart Press, Summit, New Jersey, 360pp.

D'Agostino, R.B. (1986a). Graphical Analysis. In: D'Agostino, R.B., and M.A. Stephens, eds. Goodness-of Fit Techniques. Marcel Dekker, New York, Chapter 2, pp.7–62.

Scott, D. W. (1992). Multivariate Density Estimation: Theory, Practice and Visualization. John Wiley and Sons, New York.

Sheather, S. J. and Jones M. C. (1991). A Reliable Data-Based Bandwidth Selection Method for Kernel Density Estimation. Journal of the Royal Statististical Society B, 683–690.

Silverman, B.W. (1986). Density Estimation for Statistics and Data Analysis. Chapman and Hall, London.

Wegman, E.J. (1972). Nonparametric Probability Density Estimation. Technometrics 14, 533-546.

See Also

density, approx, epdfPlot, ecdfPlot, cdfCompare, qqplot, eqnpar, quantile, sample,
simulateVector, simulateMvMatrix.

Examples

  # Create a set of 100 observations from a gamma distribution with 
  # parameters shape=4 and scale=5. 
  # (Note: the call to set.seed simply allows you to reproduce this example.)

  set.seed(3) 
  obs <- rgamma(100, shape=4, scale=5)

  # Now plot the empirical distribution (with a histogram) and the true distribution:

  dev.new()
  hist(obs, col = "cyan", xlim = c(0, 65), freq = FALSE, 
    ylab = "Relative Frequency") 

  pdfPlot('gamma', list(shape = 4, scale = 5), add = TRUE) 

  box()

  # Now plot the empirical distribution (based on demp) with the 
  # true distribution:

  x <- qemp(p = seq(0, 1, len = 100), obs = obs) 
  y <- demp(x, obs) 

  dev.new()
  plot(x, y, xlim = c(0, 65), type = "n", 
    xlab = "Value of Random Variable", 
    ylab = "Relative Frequency") 
  lines(x, y, lwd = 2, col = "cyan") 

  pdfPlot('gamma', list(shape = 4, scale = 5), add = TRUE)

  # Alternatively, you can create the above plot with the function 
  # epdfPlot:

  dev.new()
  epdfPlot(obs, xlim = c(0, 65), epdf.col = "cyan", 
    xlab = "Value of Random Variable", 
    main = "Empirical and Theoretical PDFs")

  pdfPlot('gamma', list(shape = 4, scale = 5), add = TRUE)

  


  # Clean Up
  #---------
  rm(obs, x, y)

Internal EnvStats Objects

Description

Internal EnvStats objects

Details

These are not to be called by the user. They have been exported to allow advanced users to see their structure.

Atmospheric Environmental Conditions in New York City

Description

Daily measurements of ozone concentration, wind speed, temperature, and solar radiation in New York City for 153 consecutive days between May 1 and September 30, 1973.

Usage

  Environmental.df
  Air.df

Format

The data frame Environmental.df has 153 observations on the following 4 variables.

ozone

Average ozone concentration (of hourly measurements) of in parts per billion.

radiation

Solar radiation (from 08:00 to 12:00) in langleys.

temperature

Maximum daily temperature in degrees Fahrenheit.

wind

Average wind speed (at 07:00 and 10:00) in miles per hour.

Row names are the dates the data were collected.

The data frame Air.df is the same as Environmental.df except that the column ozone is the cube root of average ozone concentration.

Details

Data on ozone (ppb), solar radiation (langleys), temperature (degrees Fahrenheit), and wind speed (mph) for 153 consecutive days between May 1 and September 30, 1973. These data are a superset of the data contained in the data frame environmental in the package lattice.

Source

Chambers et al. (1983), pp. 347-349.

References

Chambers, J.M., W.S. Cleveland, B. Kleiner, and P.A. Tukey. (1983). Graphical Methods for Data Analysis. Duxbury Press, Boston, MA, 395pp.

Cleveland, W.S. (1993). Visualizing Data. Hobart Press, Summit, New Jersey, 360pp.

Cleveland, W.S. (1994). The Elements of Graphing Data. Revised Edition. Hobart Press, Summit, New Jersey, 297pp.

Examples

# Scatterplot matrix
pairs(Environmental.df)

pairs(Air.df)


# Time series plot for ozone
attach(Environmental.df)
dates <- as.Date(row.names(Environmental.df), format = "%m/%d/%Y")
plot(dates, ozone, type = "l", 
    xlab = "Time (Year = 1973)", ylab = "Ozone (ppb)",
    main = "Time Series Plot of Daily Ozone Measures")
detach("Environmental.df")
rm(dates)

Euler's Constant

Description

Explanation of Euler's Constant.

Details

Euler's Constant, here denoted \epsilon, is a real-valued number that can be defined in several ways. Johnson et al. (1992, p. 5) use the definition:

\epsilon = \lim_{n \to \infty}[1 + \frac{1}{2} + \frac{1}{3} + \ldots + \frac{1}{n} - log(n)]

and note that it can also be expressed as

\epsilon = -\Psi(1)

where \Psi() is the digamma function (Johnson et al., 1992, p.8).

The value of Euler's Constant, to 10 decimal places, is 0.5772156649.

The expression for the mean of a Type I extreme value (Gumbel) distribution involves Euler's constant; hence Euler's constant is used to compute the method of moments estimators for this distribution (see eevd).

Author(s)

Steven P. Millard (EnvStats@ProbStatInfo.com)

References

Johnson, N. L., S. Kotz, and A.W. Kemp. (1992). Univariate Discrete Distributions. Second Edition. John Wiley and Sons, New York, pp.4-8.

Johnson, N. L., S. Kotz, and N. Balakrishnan. (1995). Continuous Univariate Distributions, Volume 2. Second Edition. John Wiley and Sons, New York.

See Also

Extreme Value Distribution, eevd.

EnvStats Functions Listed by Category

Description

Hyperlink list of EnvStats functions by category.

Details

• Calibration

• Censored Data

• Data Transformations

• Estimating Distribution Parameters

• Estimating Distribution Quantiles

• Goodness-of-Fit Tests

• Hypothesis Tests

• Monte Carlo Simulation and Risk Assessment

• Plotting Probability Distributions

• Plotting Using ggplot2

• Power and Sample Size Calculations

• Prediction Intervals

• Printing and Plotting Methods

• Probability Distributions and Random Numbers

• Summary Statistics

• Tolerance Intervals

• Trend Analysis

EnvStats Functions for Calibration

Description

The EnvStats functions listed below are useful for performing calibration and inverse prediction to determine the concentration of a chemical based on a machine signal.

Details

EnvStats Functions for Censored Data

Description

The EnvStats functions listed below are useful for dealing with Type I censored data.

Details

Data Transformations

Estimating Distribution Parameters

Estimating Distribution Quantiles

All of the functions for computing quantiles (and associated confidence intervals) for complete (uncensored) data are listed in the help file Estimating Distribution Quantiles. All of these functions, with the exception of eqnpar, will accept an object of class "estimateCensored". Thus, you may estimate quantiles (and construct approximate confidence intervals) for any distribution for which:

1. There exists a function to estimate distribution parameters using censored data (see the section Estimating Distribution Parameters above).

2. There exists a function to estimate quantiles for that distribution based on complete data (see the help file Estimating Distribution Quantiles).

Nonparametric estimates of quantiles (and associated confidence intervals) can be constructed from censored data as long as the order statistics used in the results are above all left-censored observations or below all right-censored observations. See the help file for eqnpar for more information and examples.

Goodness-of-Fit Tests

Hypothesis Tests

Plotting Probability Distributions

Prediction and Tolerance Intervals

All of the functions for computing prediction and tolerance intervals for complete (uncensored) data are listed in the help files Prediction Intervals and Tolerance Intervals. All of these functions, with the exceptions of predIntNpar and tolIntNpar, will accept an object of class "estimateCensored". Thus, you may construct approximate prediction or tolerance intervals for any distribution for which:

1. There exists a function to estimate distribution parameters using censored data (see the section Estimating Distribution Parameters above).

2. There exists a function to create a prediction or tolerance interval for that distribution based on complete data (see the help files Prediction Intervals and Tolerance Intervals).

Nonparametric prediction and tolerance intervals can be constructed from censored data as long as the order statistics used in the results are above all left-censored observations or below all right-censored observations. See the help files for predIntNpar, predIntNparSimultaneous, and tolIntNpar for more information and examples.

EnvStats Functions for Data Transformations

Description

The EnvStats functions listed below are useful for deciding on data transformations.

Details

EnvStats Functions for Estimating Distribution Parameters

Description

The EnvStats functions listed below are useful for estimating distribution parameters and optionally constructing confidence intervals.

Details

EnvStats Functions for Estimating Distribution Quantiles

Description

The EnvStats functions listed below are useful for estimating distribution quantiles and, for some functions, optionally constructing confidence intervals for a quantile.

Details

EnvStats Functions for Goodness-of-Fit Tests

Description

The EnvStats functions listed below are useful for performing goodness-of-fit tests for user-specified probability distributions.

Details

Goodness-of-Fit Tests

Tests for Outliers

Choose a Distribution

EnvStats Functions for Hypothesis Tests

Description

The EnvStats functions listed below are useful for performing hypothesis tests not already built into R. See Power and Sample Size Calculations for a list of functions you can use to perform power and sample size calculations based on various hypothesis tests.

Details

For goodness-of-fit tests, see Goodness-of-Fit Tests.

EnvStats Functions for Monte Carlo Simulation and Risk Assessment

Description

The EnvStats functions listed below are useful for performing Monte Carlo simulations and risk assessment.

Details

EnvStats Functions for Plotting Probability Distributions

Description

The EnvStats functions listed below are useful for plotting probability distributions.

Details

EnvStats Functions for Creating Plots Using the ggplot2 Package

Description

The EnvStats functions listed below are useful for creating plots with the ggplot2 package.

Details

EnvStats Functions for Power and Sample Size Calculations

Description

The EnvStats functions listed below are useful for power and sample size calculations.

Details

Confidence Intervals

Hypothesis Tests

Prediction Intervals

Normal Distribution Prediction Intervals

Lognormal Distribution Prediction Intervals

Nonparametric Prediction Intervals

Tolerance Intervals

EnvStats Functions for Prediction Intervals

Description

The EnvStats functions listed below are useful for computing prediction intervals and simultaneous prediction intervals. See Power and Sample Size for a list of functions useful for computing power and sample size for a design based on a prediction interval width, or a design based on a hypothesis test for future observations falling outside of a prediciton interval.

Details

EnvStats Functions for Printing and Plotting Objects of Various S3 Classes

Description

The EnvStats functions listed below are printing and plotting methods for various S3 classes.

Details

Printing Methods

Plotting Methods

EnvStats Probability Distributions and Random Numbers

Description

Listed below are all of the probability distributions available in R and EnvStats. Distributions with a description in bold are new ones that are part of EnvStats. For each distribution, there are functions for generating: values for the probability density function, values for the cumulative distribution function, quantiles, and random numbers.

The data frame Distribution.df contains information about all of these probability distributions.

Details