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Confidence Intervals and Tests for Two Exponential Scale Parameters Based On Order Statistics in Compressed Samples

Kenneth S. Kaminsky

Abstract

We construct confidence intervals for the ratio of two exponential scale parameters and present a test of hypothesis concerning these parameters. The procedures are based on the selection of subsets of two independent ordered samples from exponential populations. The discussion centers around the distribution of the ratio of the BLUE's (the ABLE's in large samples) of these parameters, and a simple approximation to that distribution. Optimal selection of the data is discussed. In an example, the power function of the proposed test is compared with the power function of the same test based on complete samples.

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Key concepts: Statistics, Mathematics, Exponential function, Confidence interval, Exponential distribution, Selection (genetic algorithm), Power function, Order statistic