Bayesian inference of dynamic cumulative residual entropy from Pareto Ⅱ distribution with application to COVID-19

Abdullah Ali H. Ahmadini; Amal S. Hassan; Ahmed N. Zaky; Shokrya S. Alshqaq; Abdullah Ali H. Ahmadini; Amal S. Hassan; Ahmed N. Zaky; Shokrya S. Alshqaq

doi:10.3934/math.2021133

AIMS Mathematics

2021, Volume 6, Issue 3: 2196-2216. doi: 10.3934/math.2021133

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Research article

Bayesian inference of dynamic cumulative residual entropy from Pareto Ⅱ distribution with application to COVID-19

1.
Department of Mathematics, Faculty of Science, Jazan University, Jazan, Saudi Arabia
2.
Faculty of Graduate Studies for Statistical Research, Cairo University, Egypt
3.
Institute of National Planning, Egypt
4.
Department of Mathematics, Faculty of Science, Jazan University, Jazan, Saudi Arabia

Received: 20 October 2020 Accepted: 08 December 2020 Published: 11 December 2020
MSC : 62F15, 94A17, 94A24

Dynamic cumulative residual entropy is a recent measure of uncertainty which plays a substantial role in reliability and survival studies. This article comes up with Bayesian estimation of the dynamic cumulative residual entropy of Pareto Ⅱ distribution in case of non-informative and informative priors. The Bayesian estimator and the corresponding credible interval are obtained under squared error, linear exponential (LINEX) and precautionary loss functions. The Metropolis-Hastings algorithm is employed to generate Markov chain Monte Carlo samples from the posterior distribution. A simulation study is done to implement and compare the accuracy of considered estimates in terms of their relative absolute bias, estimated risk and the width of credible intervals. Regarding the outputs of simulation study, Bayesian estimate of dynamic cumulative residual entropy under LINEX loss function is preferable than the other estimates in most of situations. Further, the estimated risks of dynamic cumulative residual entropy decrease as the value of estimated entropy decreases. Eventually, inferential procedure developed in this paper is illustrated via a real data.
- Shannon entropy,
- dynamic cumulative residual entropy,
- Pareto Ⅱ distribution,
- Bayesian estimators,
- loss functions
Citation: Abdullah Ali H. Ahmadini, Amal S. Hassan, Ahmed N. Zaky, Shokrya S. Alshqaq. Bayesian inference of dynamic cumulative residual entropy from Pareto Ⅱ distribution with application to COVID-19[J]. AIMS Mathematics, 2021, 6(3): 2196-2216. doi: 10.3934/math.2021133

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Abstract

Dynamic cumulative residual entropy is a recent measure of uncertainty which plays a substantial role in reliability and survival studies. This article comes up with Bayesian estimation of the dynamic cumulative residual entropy of Pareto Ⅱ distribution in case of non-informative and informative priors. The Bayesian estimator and the corresponding credible interval are obtained under squared error, linear exponential (LINEX) and precautionary loss functions. The Metropolis-Hastings algorithm is employed to generate Markov chain Monte Carlo samples from the posterior distribution. A simulation study is done to implement and compare the accuracy of considered estimates in terms of their relative absolute bias, estimated risk and the width of credible intervals. Regarding the outputs of simulation study, Bayesian estimate of dynamic cumulative residual entropy under LINEX loss function is preferable than the other estimates in most of situations. Further, the estimated risks of dynamic cumulative residual entropy decrease as the value of estimated entropy decreases. Eventually, inferential procedure developed in this paper is illustrated via a real data.

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