cenTolInt function

Upper Tolerance interval for censored data

Computes a one-sided upper tolerance interval for censored data assuming log-normal, gamma and normal distributions.

cenTolInt(
  x.var,
  cens.var,
  conf = 0.95,
  cover = 0.9,
  method.fit = "mle",
  printstat = TRUE
)

Arguments

• x.var: The column of x (response variable) values plus detection limits
• cens.var: The column of indicators, where 1 (or TRUE) indicates a detection limit in the y.var column, and 0 (or FALSE) indicates a detected value in y.var.
• conf: Confidence coefficient of the interval, 0.95 (default).
• cover: Coverage, the percentile probability above which the tolerance interval is computed. The default is 90, so a tolerance interval will be computed above the 90th percentile of the data.
• method.fit: The method used to compute the parameters of the distribution. The default is maximum likelihood (“mle”). The alternative is robust ROS (“rROS”). See Details.
• printstat: Logical TRUE/FALSE option of whether to print the resulting statistics in the console window, or not. Default is TRUE.

Returns

Prints and returns the percentile (cover), upper tolerance limit (conf) and BIC of fit for lognormal, normal and approximated gamma distributions. Plots empirical and theoretical CDFs with BIC values in the legend.

Details

Computes upper one-sided tolerance intervals for three distributions. This is a front-end to the individual functions from the EnvStats package. By default all three are computed using maximum likelihood estimation (mle); robust ROS is available as an alternate method for all three distributions. The gamma distribution for censored data uses the Wilson-Hilferty approximation (normal distribution on cube roots of data). For more info on the relative merits of robust ROS versus mle, see Helsel (2011) and Millard (2013).

Examples

data(PbHeron)

# Default
cenTolInt(PbHeron$Liver,PbHeron$LiverCen)

# User defined conficence interval
cenTolInt(PbHeron$Liver,PbHeron$LiverCen,conf=0.75)

# User defined percentile
cenTolInt(PbHeron$Liver,PbHeron$LiverCen,cover=0.5)

# inputs outside acceptable ranges
# Will result in errors/warnings
# cenTolInt(PbHeron$Liver,PbHeron$LiverCen,cover=1.25)
# cenTolInt(PbHeron$Liver,PbHeron$LiverCen,conf=1.1)
# cenTolInt(PbHeron$Liver,PbHeron$LiverCen,method.fit="ROS")

References

Helsel, D.R., 2011. Statistics for censored environmental data using Minitab and R, 2nd ed. John Wiley & Sons, USA, N.J.

Millard, S.P., 2013. EnvStats: An R Package for Environmental Statistics. Springer-Verlag, New York.

Krishnamoorthy, K., Mathew, T., Mukherjee, S., 2008. Normal-Based Methods for a Gamma Distribution, Technometrics, 50, 69-78.