Testing for the Goodness of Fit for the DMRL Class of Life Distributions

Tanusri Ray () and Debasis Sengupta ()
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Tanusri Ray: Maharaja Manindra Chandra College
Debasis Sengupta: Indian Statistical Institute

A chapter in Strategic Management, Decision Theory, and Decision Science, 2021, pp 119-143 from Springer

Abstract: Abstract Nonparametric classes of life distributions indicating various types of ageing have been studied by reliability theorists for more than half a century. When a distribution happens to belong to one such class, several inequalities and probabilistic bounds become applicable. On the other hand, membership in a class may have to be verified empirically. The decreasing mean residual life (DMRL) class of distributions is a case in point. There have been a number of tests of the exponential distributions against the DMRL alternative. In order to complement these, we propose a test of membership to the DMRL class, with the class of non-DMRL distributions as the alternative hypothesis. The proposed test is based on the integrated mean residual life function, which should be concave for the DMRL class. The gap between the empirical version of this function and its least concave majorant is used as the test statistic. Computer simulations indicate that the exponential distribution may be the least favorable distribution within the null hypothesis, and a conservative test may be carried out from simulated values of the statistic under that distribution. The aim of this work is to demonstrate how the proposed test, together with the existing tests of exponentiality against the DMRL alternative, can be used to determine for sure whether a life distribution can be empirically classified as DMRL.

Keywords: Mean residual life; Least concave majorant; Conservative test; Least favorable distribution; Primary 62N05; Secondary 62G10; 62N03 (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-16-1368-5_9

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DOI: 10.1007/978-981-16-1368-5_9

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