The exact null distribution of the generalized Hollander-Proschan type test for NBUE alternatives

TL;DR

This paper derives the exact null distribution for a test statistic used to identify NBUE alternatives, improving the accuracy of hypothesis testing in reliability analysis.

Contribution

It provides the exact null distribution for the Hollander-Proschan type test, including tabulated critical values, enhancing test precision over approximate methods.

Findings

Exact null distribution derived for the test statistic.

Tabulated critical values for different significance levels.

Remarks on advantages of using the exact distribution.

Abstract

In this note we derive the exact null distribution for the test statistic proposed by Anis and Mitra (2011) for testing exponentiality against NBUE alternatives. As a special case, we obtain the exact null distribution for the test statistic proposed by Hollander and Proschan (1975). Selected critical values for different size are tabulated for these two statistics. Some remarks concerning the benefits of using the exact distribution are made.