Tests for exponentiality against NBUE alternatives: a Monte Carlo comparison

TL;DR

This paper compares various statistical tests for exponentiality against NBUE alternatives using Monte Carlo simulations to evaluate their size and power across different sample sizes.

Contribution

It provides a comprehensive Monte Carlo comparison of tests for exponentiality against NBUE, offering guidance on test selection based on alternative suspicion.

Findings

Empirical sizes of tests are obtained through simulations.

Power comparisons highlight the most effective tests for various alternatives.

Recommendations are provided for choosing tests based on suspected alternatives.

Abstract

Testing of various classes of life distributions has been addressed in the literature for more than 45 years. In this paper, we consider the problem of testing exponentiality (which essentially implies no ageing) against positive ageing which is captured by the fairly large class of new better than used in expectation (NBUE) distributions. These tests of exponentiality against NBUE alternatives are discussed and compared. The empirical size of the tests is obtained by simulations. Power comparisons for different popular alternatives are done using Monte Carlo simulations. These comparisons are made for both small and large sample sizes. The paper concludes with a discussion in which suggestions are made regarding the choices of the test when a particular alternative is suspected.