Fiducial-based tolerance intervals for some discrete distributions

Fiducial quantities are proposed to construct approximate tolerance limits and intervals for functions of some discrete random variables. Using established fiducial quantities for binomial proportions, Poisson rates, and negative binomial proportions, an approach is demonstrated to handle functions of discrete random variables, whose distributions are either not available or are intractable. The construction of tolerance intervals using fiducial quantities is straightforward and, thus, amenable to numerical computation. An extensive numerical study shows that for most settings of the cases considered, the coverage probabilities are near the nominal levels. The applicability of the method is further demonstrated using four real datasets, including a discussion of the corresponding software that is available for the R programming language.