Bounds for the Varentropy of Basic Discrete Distributions and Characterization of Some Discrete Distributions

Document Type : Original Research Articles

Author
Faranak Goodarzi
Department of Statistics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Islamic Republic of Iran
10.22059/jsciences.2025.379169.1007870
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 a 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.
Keywords
Varentropy
Reversed hazard rate
Binomial transform
Cauchy-Schwarz inequality
Subjects
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Journal of Sciences, Islamic Republic of Iran
Volume 35, Issue 3
Summer 2024
Pages 233-241