Dynamic cumulative residual Rényi entropy for Lomax distribution: Bayesian and non-Bayesian methods

Abdulhakim A. Al-Babtain; Amal S. Hassan; Ahmed N. Zaky; Ibrahim Elbatal; Mohammed Elgarhy; Abdulhakim A. Al-Babtain; Amal S. Hassan; Ahmed N. Zaky; Ibrahim Elbatal; Mohammed Elgarhy

doi:10.3934/math.2021231

AIMS Mathematics

2021, Volume 6, Issue 4: 3889-3914. doi: 10.3934/math.2021231

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Research article

Dynamic cumulative residual Rényi entropy for Lomax distribution: Bayesian and non-Bayesian methods

1.
Department of Statistics and Operations Research, King Saud University, Riyadh 11362, Saudi Arabia
2.
Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt
3.
Institute of National Planning, Cairo 11765, Egypt
4.
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
5.
The Higher Institute of Commercial Sciences, Al Mahalla Al Kubra, Algarbia 31951, Egypt

Received: 18 October 2020 Accepted: 21 January 2021 Published: 02 February 2021
MSC : 62G07, 62C05, 62E20

An alternative measure of uncertainty related to residual lifetime function is the dynamic cumulative residual entropy which plays a significant role in reliability and survival analysis. This article deals with estimating dynamic cumulative residual Rényi entropy (DCRRE) for Lomax distribution using maximum likelihood and Bayesian methods of estimation. The maximum likelihood estimates and approximate confidence intervals of DCRRE are derived. Bayesian estimates and Bayesian credible intervals are derived based on gamma priors for the DCRRE 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 distributions. The Bayes estimates are compared through Monte Carlo simulations. Regarding simulation results, we observe that the maximum likelihood and Bayesian estimates of the DCRRE are decreasing function on time. Further, maximum likelihood and Bayesian estimates of the DCRRE perform well as the sample size increases. Bayesian estimate of the DCRRE under LINEX loss function is more convenient than the other estimates in the most of the situations. Real data set is analyzed for clarifying purposes.
- dynamic cumulative residual Rényi entropy,
- Lomax distribution,
- Bayesian estimates,
- loss function
Citation: Abdulhakim A. Al-Babtain, Amal S. Hassan, Ahmed N. Zaky, Ibrahim Elbatal, Mohammed Elgarhy. Dynamic cumulative residual Rényi entropy for Lomax distribution: Bayesian and non-Bayesian methods[J]. AIMS Mathematics, 2021, 6(4): 3889-3914. doi: 10.3934/math.2021231

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Abstract

An alternative measure of uncertainty related to residual lifetime function is the dynamic cumulative residual entropy which plays a significant role in reliability and survival analysis. This article deals with estimating dynamic cumulative residual Rényi entropy (DCRRE) for Lomax distribution using maximum likelihood and Bayesian methods of estimation. The maximum likelihood estimates and approximate confidence intervals of DCRRE are derived. Bayesian estimates and Bayesian credible intervals are derived based on gamma priors for the DCRRE 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 distributions. The Bayes estimates are compared through Monte Carlo simulations. Regarding simulation results, we observe that the maximum likelihood and Bayesian estimates of the DCRRE are decreasing function on time. Further, maximum likelihood and Bayesian estimates of the DCRRE perform well as the sample size increases. Bayesian estimate of the DCRRE under LINEX loss function is more convenient than the other estimates in the most of the situations. Real data set is analyzed for clarifying purposes.

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