Bayesian Estimation of Dynamic Cumulative Residual Entropy for Classical Pareto Distribution

Renjini, K.R.; Sathar, E. I. Abdul; Rajesh, G.

doi:10.1080/01966324.2017.1364184

Cited by 8 publications

(5 citation statements)

References 18 publications

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“…Here, we consider several asymmetric and symmetric loss functions including: squared error loss function (SELF), modified squared error loss function (MSELF), weighted squared error loss function (WSELF), K-loss function (KLF), linear exponential loss function (LINEXLF), precautionary loss function (PLF) and general entropy loss function (GELF). For more details, see [25] and the references therein. In Table 1, we provide a summary of these loss functions and associated Bayesian estimators and posterior risks.…”

Section: Bayesian Inference Of Regression Modelmentioning

confidence: 99%

Arctan-Based Family of Distributions: Properties, Survival Regression, Bayesian Analysis and Applications

Kharazmi

Alizadeh

Contreras-Reyes

et al. 2022

Axioms

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In this paper, a new class of the continuous distributions is established via compounding the arctangent function with a generalized log-logistic class of distributions. Some structural properties of the suggested model such as distribution function, hazard function, quantile function, asymptotics and a useful expansion for the new class are given in a general setting. Two special cases of this new class are considered by employing Weibull and normal distributions as the parent distribution. Further, we derive a survival regression model based on a sub-model with Weibull parent distribution and then estimate the parameters of the proposed regression model making use of Bayesian and frequentist approaches. We consider seven loss functions, namely the squared error, modified squared error, weighted squared error, K-loss, linear exponential, general entropy, and precautionary loss functions for Bayesian discussion. Bayesian numerical results include a Bayes estimator, associated posterior risk, credible and highest posterior density intervals are provided. In order to explore the consistency property of the maximum likelihood estimators, a simulation study is presented via Monte Carlo procedure. The parameters of two sub-models are estimated with maximum likelihood and the usefulness of these sub-models and a proposed survival regression model is examined by means of three real datasets.

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Section: Bayesian Inference Of Regression Modelmentioning

confidence: 99%

Arctan-Based Family of Distributions: Properties, Survival Regression, Bayesian Analysis and Applications

Kharazmi

Alizadeh

Contreras-Reyes

et al. 2022

Axioms

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“…, is survival function of t. If an item has been sustained up to time t then DCRE measures the uncertainty in its remaining life. The application and properties of DCRE are discussed by Asadi and Zohrevand [3], Navarro et al [13], and Renjini et al [16]. For classical Pareto distribution, the Bayesian estimation of dynamic cumulative residual entropy was intended by Renjini et al [16].…”

Section: Introductionmentioning

confidence: 99%

“…The application and properties of DCRE are discussed by Asadi and Zohrevand [3], Navarro et al [13], and Renjini et al [16]. For classical Pareto distribution, the Bayesian estimation of dynamic cumulative residual entropy was intended by Renjini et al [16]. The aim of this paper is to study estimators of dynamic cumulative residual entropy (DCRE) of Pareto type II distribution using Bayesian techniques as discussed in Renjini et al [16].…”

Section: Introductionmentioning

confidence: 99%

“…For classical Pareto distribution, the Bayesian estimation of dynamic cumulative residual entropy was intended by Renjini et al [16]. The aim of this paper is to study estimators of dynamic cumulative residual entropy (DCRE) of Pareto type II distribution using Bayesian techniques as discussed in Renjini et al [16]. The DCRE for (1.1) is simplified as…”

Section: Introductionmentioning

confidence: 99%

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Bayesian Estimators of Dynamic Cumulative Residual Entropy for Pareto Type II Distribution

Savita¹,

Kumar²

2022

Comm. Math. Appl.

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In this paper, Pareto type II distribution is used to propose Bayes estimator of dynamic cumulative residual entropy. To calculate posterior risks, various informative and non-informative priors are used. Using different loss functions, Bayes estimators and associated posterior risks for the distribution have been calculated. Numerical computation is carried out with the help of a real data set. In the last, Monte Carlo Simulation study and Graphical analysis are also given along with the conclusion drawn.

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“…The cumulative residual and past inaccuracy have been proposed in [16] as extensions of the cumulative entropies for the truncated random variables. The Bayesian estimators of the DCR entropy of the Pareto model using different sampling schemes have been studied in [17][18][19]. The Bayesian inference of the DCR entropy for the Pareto II distribution was given in [20].…”

Section: Introductionmentioning

confidence: 99%

Bayesian Analysis of Dynamic Cumulative Residual Entropy for Lindley Distribution

Almarashi

Algarni

Hassan

et al. 2021

Entropy

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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.

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Bayesian Estimation of Dynamic Cumulative Residual Entropy for Classical Pareto Distribution

Cited by 8 publications

References 18 publications

Arctan-Based Family of Distributions: Properties, Survival Regression, Bayesian Analysis and Applications

Arctan-Based Family of Distributions: Properties, Survival Regression, Bayesian Analysis and Applications

Bayesian Estimators of Dynamic Cumulative Residual Entropy for Pareto Type II Distribution

Bayesian Analysis of Dynamic Cumulative Residual Entropy for Lindley Distribution

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