Testing for exponentiality for stationary associated random variables

TL;DR

This paper investigates how to test for exponential distribution in stationary associated random variables, analyzing the asymptotic behavior of existing tests under dependence and illustrating their performance through simulations.

Contribution

It extends the understanding of exponentiality tests to dependent data, specifically stationary associated variables, and evaluates their asymptotic properties and effectiveness.

Findings

Dependence affects the asymptotic normality of test statistics.

Dependence influences the size and power of the tests.

Simulation results demonstrate the impact of dependence on test performance.

Abstract

In this paper, we consider the problem of testing for exponentiality against univariate positive ageing when the underlying sample consists of stationary associated random variables. In particular, we discuss the asymptotic behavior of the tests by Deshpande (1983), Hollander and Proschan (1972) and Ahmad (1992) for testing exponentiality against IFRA, NBU and DMRL, respectively under association. A simulation study illustrates the effect of dependence on the asymptotic normality of the test statistics and on the size and power of the tests.