A review of tests for exponentiality with Monte Carlo comparisons

Abstract

In this paper, 91 different tests for exponentiality are reviewed. Some of the tests are universally consistent while others are against some special classes of life distributions. Power performances of 40 of these different tests for exponentiality of datasets are compared through extensive Monte Carlo simulations. The comparisons are conducted for different sample sizes of 10, 25, 50 and 100 for different groups of distributions according to the shape of their hazard functions at 5 percent level of significance. Also, the techniques are applied to two real-world datasets and a measure of power is employed for the comparison of the tests. The results show that some tests which are very good under one group of alternative distributions are not so under another group. Also, some tests maintained relatively high power over all the groups of alternative distributions studied while some others maintained poor power performances over all the groups of alternative distributions. Again, the result obtained from real-world datasets agree completely with those of the simulation studies.

KEYWORDS:

• Classes of life distributions
• empirical power of a test
• exponentiality
• goodness-of-fit test
• Monte Carlo simulation

Subject Classifications:

• 62E10
• 62E20
• 62F03

Acknowledgements

The authors are very grateful to the two anonymous reviewers and the associate editor for their valuable comments which have greatly improved this comparative review article.

Disclosure statement

No potential conflict of interest was reported by the author(s).