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Varentropy of doubly truncated random variable

Part of: Sufficiency and information Survival analysis and censored data Communication, information

Published online by Cambridge University Press:  08 July 2022

Akash Sharma  and
Chanchal Kundu Open the ORCID record for Chanchal Kundu [Opens in a new window]
Akash Sharma
Affiliation:
Department of Mathematical Sciences, Rajiv Gandhi Institute of Petroleum Technology, Jais 229304, UP, India. E-mails: chanchal_kundu@yahoo.com, ckundu@rgipt.ac.in
Chanchal Kundu
Affiliation:
Department of Mathematical Sciences, Rajiv Gandhi Institute of Petroleum Technology, Jais 229304, UP, India. E-mails: chanchal_kundu@yahoo.com, ckundu@rgipt.ac.in
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Abstract

Recently, there is a growing interest to study the variability of uncertainty measure in information theory. For the sake of analyzing such interest, varentropy has been introduced and examined for one-sided truncated random variables. As the interval entropy measure is instrumental in summarizing various system and its components properties when it fails between two time points, exploring variability of such measure pronounces the extracted information. In this article, we introduce the concept of varentropy for doubly truncated random variable. A detailed study of theoretical results taking into account transformations, monotonicity and other conditions is proposed. A simulation study has been carried out to investigate the behavior of varentropy in shrinking interval for simulated and real-life data sets. Furthermore, applications related to the choice of most acceptable system and the first-passage times of an Ornstein–Uhlenbeck jump-diffusion process are illustrated.

Keywords

Doubly truncated random variableInterval varentropyParametric form of GFRVarentropy

MSC classification

Primary: 94A17: Measures of information, entropy
Secondary: 62B10: Information-theoretic topics 62N05: Reliability and life testing
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 37 , Issue 3 , July 2023 , pp. 852 - 871
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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