Bayesian Analysis of Dynamic Cumulative Residual Entropy for Lindley Distribution.

Abdullah M Almarashi,Ahmed N Zaky,Ali Algarni,Mohammed Elgarhy,Amal S Hassan

doi:10.3390/e23101256

Abdullah M Almarashi, Ahmed N Zaky + Show 3 more

Open Access

https://doi.org/10.3390/e23101256

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Journal: Entropy	Publication Date: Sep 27, 2021
Citations: 4	License type: CC BY 4.0

Affiliation: King Abdulaziz University, Cairo University

Abstract

Dynamic cumulative residual (DCR) entropy is a valuable randomness metric that may be used in survival analysis. The Bayesian estimator of the DCR Rényi entropy (DCRRéE) for the Lindley distribution using the gamma prior is discussed in this article. Using a number of selective loss functions, the Bayesian estimator and the Bayesian credible interval are calculated. In order to compare the theoretical results, a Monte Carlo simulation experiment is proposed. Generally, we note that for a small true value of the DCRRéE, the Bayesian estimates under the linear exponential loss function are favorable compared to the others based on this simulation study. Furthermore, for large true values of the DCRRéE, the Bayesian estimate under the precautionary loss function is more suitable than the others. The Bayesian estimates of the DCRRéE work well when increasing the sample size. Real-world data is evaluated for further clarification, allowing the theoretical results to be validated.

Highlights

Reference [1] introduced the idea of the Rényi entropy as a measure of randomness for Y
We outline the paper as follows: Section 2 gives the formula for the DCR Rényi entropy (DCRRéE) of the Lindley distribution; Section 3 offers the DCRRéE’s Bayesian estimator of the Lindley distribution under the specific loss functions; a description of Markov Chain Monte Carlo (MCMoC) is provided in Section 4; and in Section 5, a real-world data application is shown
For the Lindley distribution at β = 0.5, a numerical analysis is conducted in this part to examine the performance of the Bayesian estimates of γR(β)

Summary

Introduction

Reference [1] introduced the idea of the Rényi entropy as a measure of randomness for Y. The Bayesian estimators of the DCR entropy of the Pareto model using different sampling schemes have been studied in [17,18,19]. To generate random numbers from the Lindley distribution, we may use the fact that the distribution, as given in Equation (3), is a mixture of exponential (θ) and gamma (2, θ), with mixing proportions (θ/1 + θ) and (1/1 + θ), respectively. We outline the paper as follows: Section 2 gives the formula for the DCRRéE of the Lindley distribution; Section 3 offers the DCRRéE’s Bayesian estimator of the Lindley distribution under the specific loss functions; a description of MCMoC is provided in Section 4; and, a real-world data application is shown. Using the findings of our numerical investigations, we came to certain conclusions

Expression of the DCRRéE for the Lindley Distribution

The Bayesian Estimation

Numerical Illustrations and Results

Numerical Results

Application