Censored Kullback-Leibler Information and Goodness-of-Fit Test with Type II Censored Data

Abstract

The Kulback-Leibler information has been considered for establishing goodness-of-fit test statistics, which have been shown to perform very well (Arizono & Ohta, 1989; Ebrahimi et al., 1992, etc). In this paper, we propose censored Kullback-Leibler information to generalize the discussion of the Kullback-Leibler information to the censored case. Then we establish a goodness-of-fit test statistic based on the censored Kullback-Leibler information with the type 2 censored data, and compare the test statistics with some existing test statistics for the exponential and normal distributions.Entropy difference, maximum entropy distribution, minimum discrimination information loss estimation, order statistics, sample entropy,

Shannon's Entropy and Its Generalisations Towards Statistical Inference in Last Seven Decades

“…Test for location scale and shape families using KL divergence is discussed in Noughabi and Argghami (2013). KL divergence is used for testing of hypotheses based on type II censored data by Lim and Park (2007; 2015). It has been used to test a given value of Shannon's entropy of discrete finite range distributions by Girardin and Regnault (2016).…”

An Updated Review of Goodness of Fit Tests Based on Entropy

“…Other authors such as Lim and Park (2007), Balakrishnan et al (2007), Yousefzadeh and Arghami (2008), Habibi Rad et al (2011), Alizadeh Noughabi (2017c, Alizadeh Noughabi (2019), and Alizadeh Noughabi and Chahkandi (2018) introduced some tests under different censoring schemes based on entropy or censored KL Information.…”

Goodness of Fit Using a New Estimate of Kullback-Leibler Information Based on Type II Censored Data

“…So, an estimate of KL information has been used as a test statistic for goodness of fit purposes. For example, Arizono and Ohta [12], Ebrahimi et al [13], Park and Park [14], and Alizadeh Noughabi and Arghami [15] have discussed such tests for complete samples, while Balakrishnan et al [10], Lim and Park [16], Lin et al [17], Castro-Kuriss [18], Habibi Rad et al [19], Grané [20], Pakyari and Balakrishnan [21], and Park and Lim [22] developed tests based on censored samples. Moreover, Ebrahimi [23] considered the problem of testing the goodness of fit for the exponentiality of the remaining life of a system at a certain age.…”