Construction of Tolerance Bounds for the Extreme-Value and Weibull Distributions

Abstract

A method of finding confidence borunds on the percentiles of the two-parameter Weibull or extreme-value distributions is presented. The procedures, which arise from considering the distribution of parameter estimates given the observed value of an ancillary statistic, do not require the constuction of any tables, and are applicable whether the data are complete or Type II censored. The procedures also allow an investigation to be made into the adequacy of approximate confidence bounds based on an F approximation presented in Mann, Schafer and Singptuwalla [13], and those based on large sample theory for the maximum likelihood estimates.