Testing Exponentiality Based on the Lin-Wong Divergence on the Residual Lifetime Data

AuthorsFatemeh Yousefzadeh,,
JournalJournal of the Iranian Statistical Society
Page number39-61
Serial number18
Volume number2
Paper TypeFull Paper
Published At2019
Journal GradeScientific - research
Journal TypeTypographic
Journal CountryIran, Islamic Republic Of
Journal Indexisc،Scopus

Abstract

Testing exponentiality has long been an interesting issue in statistical inferences. The present article is based on a modified measure of distance between two distributions. The proposed new measure is similar to the Kullback-Leibler divergence and it is related to the Lin-Wong divergence applied on the residual lifetime data. A modified measure is developed here which is a consistent test statistic for testing the hypothesis of exponentiality against some alternatives. First, we consider a method similar to Vasicek's and Correa's techniques of estimating the density function in order to construct statistic for LW divergence. Then the critical values of the test are computed, using a Monte-Carlo simulation method. Also, we find the differences of exponential distribution detection power between the proposed test and other tests. It is shown that the proposed test performs better than other tests of exponentiality when the hazard rate is in the form of an increasing function. Finally, a case of application of the proposed test is shown through two illustrative examples.

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tags: Anderson-Darling Statistic, Correa's Technique, Cramer-von Mises Statistic, Exponentiality Test, Goodness of Fit Testing, Kolmogorov-Smirnov Statistic, Kullback-Leibler Divergence, Lin-Wong Divergence, Residual Lifetime Data, Vasicek's Technique, Zhang'