Document Type : Original Paper
Author
Faculty of Mathematical Sciences, Department of Statistics, University of kashan, Kashan, Iran
Abstract
Given the importance of varentropy in information theory, and since a closed form cannot be derived for some discrete distributions, we aim to establish bounds for the varentropy of these distributions and introduce the past varentropy for discrete random variables. In this article, we first acquired lower and upper bounds for the varentropy of the Poisson, binomial, negative binomial, and hypergeometric distributions. Since the resulting upper bounds are expressed as squared logarithmic expectations, we provide an equivalent formulation using squared logarithmic difference coefficients. Similarly, we present lower bounds in terms of logarithmic difference coefficients. Furthermore, an upper bound is derived for the variance of function of discrete reversed residual lifetime function. We also investigate inequalities involving moments of selected functions via the reversed hazard rate and characterize certain discrete distributions by the Cauchy-Schwarz inequality.
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