Selection Rules for Exponential Population Threshold Parameters

This article constructs statistical selection procedures for exponential populations that may differ in only the threshold parameters. The scale parameters of the populations are assumed common and known. The independent samples drawn from the populations are taken to be of the same size. The best population is defined as the one associated with the largest threshold parameter. In case more than one population share the largest threshold, one of these is tagged at random and denoted the best. Two procedures are developed for choosing a subset of the populations having the property that the chosen subset contains the best population with a prescribed probability. One procedure is based on the sample minimum values drawn from the populations, and another is based on the sample means from the populations. An “Indifference Zone” (IZ) selection procedure is also developed based on the sample minimum values. The IZ procedure asserts that the population with the largest test statistic (e.g., the sample minimum) is the best population. With this approach, the sample size is chosen so as to guarantee that the probability of a correct selection is no less than a prescribed probability in the parameter region where the largest threshold is at least a prescribed amount larger than the remaining thresholds. Numerical examples are given, and the computer R-codes for all calculations are given in the Appendices.