Quantile based entropy function in past lifetime

Abstract

a b s t r a c tDi Crescenzo and Longobardi (2002) introduced a measure of uncertainty in past lifetime distributions and studied its relationship with residual entropy function. In the present paper, we introduce a quantile version of the entropy function in past lifetime and study its properties. Unlike the measure of uncertainty given in Di Crescenzo and Longobardi (2002) the proposed measure uniquely determines the underlying probability distribution. The measure is used to study two nonparametric classes of distributions. We prove characterizations theorems for some well known quantile lifetime distributions.

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“…The upper bounds given in(29),(27), and (28), the cumulative past Kullback-Leibler information shown in(30), and the lower bounds provided in(26) and(25)for Example 4.1 (from top to bottom) for c 1 = 5 and c 2 = 1.…”

Further results on closure properties of LPQE order

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