Testing Exponentiality Against IDMRL Distributions with Unknown Change Point

Abstract

Guess, Hollander and Proschan proposed tests for exponentiality versus IDMRL (increasing initially and then decreasing mean residual life) distributions when the change point, or corresponding quantile, is known. In this paper we propose two tests which do not require such knowledge of the change point. The tests are based on estimates of functionals of the $\operatorname{cdf}$ which discriminate between the exponential and IDMRL families.