Monte Carlo Comparison of Approximate Tolerance Intervals for the Poisson Distribution

Abstract

The problem of finding tolerance intervals receives very much attention of researchers and are widely used in various statistical fields, including biometry, economics, reliability analysis and quality control. Tolerance interval is a random interval that covers a specified proportion of the population with a specified confidence level. In this paper, we compare approximate tolerance intervals for the Poisson random variable. Approximate tolerance intervals are constructed based on approximate confidence intervals for the parameter of the Poisson distribution such as Wald interval, Wald interval with continuity correction, score interval, variance stabilizing interval, recentered variance stabilizing interval and Freeman and Tukey interval. Coverage probabilities and expected widths of the proposed tolerance intervals are evaluated by a simulation. Proposed tolerance intervals are used by using an application example.

Keywords

• poisson distribution
• confidence interval
• tolerance interval