Page 12 - Contributed Paper Session (CPS) - Volume 3

CPS1923 Deemat C M. et al.

Test for exponentiality against renewal
increasing mean residual life class
3
Deemat C Mathew ; Sudheesh K Kattumannil , Anisha P
1
2
1 St. Thomas College Palai, Kottayam, India
2 Indian Statistical Institute, Chennai, India
3 Institute of Public Health, United Arab Emirates University, UAE

Abstract
In this paper, we develop an exact test for testing exponentiality against
renewal increasing mean residual life class. Asymptotic properties of the test
statistic are studied. Numerical results are presented to demonstrate the
performance of the testing method and we illustrate the test procedure using
a real data.

Keywords
Exponential distribution; Renewal increasing mean residual life; U-statistics

1. Introduction
Due to its importance in the analysis of age replacement model, testing
the null hypothesis that a lifetime is exponential (ageless) against the
alternatives that it has decreasing (increasing) mean residual life (MRL) class
has received considerable attention during the last two decades. Hollander
and Proschan (1975) developed a test for exponentiality against DMRL
alternative. Chen et al. (1983) extended Hollander and Proschans test to the
case of randomly right censored data. Bergman and Klesfjo (1989) developed
a family of test statistics for testing exponentiality against DMRL when the data
is both complete and censored. For recent review of different test procedure
we refer to Henze and Meintanis (2005).
If a device is experiencing a random number of shocks governed by a
homogeneous Poisson process, then renewal increasing mean residual life is
useful concept to study age replacement model. In this context testing
exponentiality against renewal increasing mean residual life shock class can be
used to determine whether to adopt a planned replacement model over
unscheduled one.
Sepehrifar et al. (2015) developed a non-parametric test against
RIMRL ℎ class and obtained a critical region based on the asymptotic
theory of U-statistics. Motivated by Sepehrifar et al. (2015), we develop an
exact test for testing exponentiality against RIMRL ℎ class. We also obtain
the critical region of the asymptotical test proposed by Sepehrifar et al. (2015)
and then find the Pitman’s asymptotic efficacy to find the performance of the
asymptotic test.

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