An adjusted cumulative Kullback-Leibler information with application to test of exponentiality

Younes Zohrevand, Reza Hashemi and Majid Asadi

Communications in Statistics - Theory and Methods, 2020, vol. 49, issue 1, 44-60

Abstract: In order to discriminate between two probability distributions extensions of Kullback–Leibler (KL) information have been proposed in the literature. In recent years, an extension called cumulative Kullback–Leibler (CKL) information is considered by authors which is closely related to equilibrium distributions. In this paper, we propose an adjusted version of CKL based on equilibrium distributions. Some properties of the proposed measure of divergence are investigated. A test of exponentiality based on the adjusted measure, is proposed. The empirical power of the presented test is calculated and compared with some existing standard tests of exponentiality. The results show that our proposed test, for some important alternative distributions, has better performance than some of the existing tests.

Date: 2020
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DOI: 10.1080/03610926.2018.1529243

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