Abstract: Tolerance intervals are widely used in industrial applications. So far attention has been mainly focused on the construction of tolerance intervals for continuous distributions. In this paper we introduce a unified analytical approach to the construction of tolerance intervals for discrete distributions in exponential families with quadratic variance functions. These tolerance intervals are shown to have desirable probability matching properties and outperform existing tolerance intervals in the literature.
Key words and phrases: Coverage probability, Edgeworth expansion, exponential family, probability matching, tolerance interval.