General Entropy with Bayes Techniques under Lindley and MCMC for Estimating the New Weibull–Pareto Parameters: Theory and Application

Eliwa, Mohamed S.; EL‐Sagheer, Rashad M.; El-Essawy, Samah H.; Almohaimeed, Bader; Alshammari, Fahad Sameer; El-Morshedy, Mahmoud

doi:10.3390/sym14112395

Cited by 2 publications

(2 citation statements)

References 31 publications

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“…Elbatal et al [8] addressed parameter estimation for the Nadarajah-Haghighi distribution with progressive Type-1 censoring, employing the squared error loss function to produce Bayes estimates and credible intervals for maximum posterior density. Eliwa et al [9] utilized balanced linear exponential and general entropy loss functions to estimate parameters for the new Weibull-Pareto distribution. Similarly, Abdel-Aty et al [10] applied squared error, LINEX, and general entropy loss functions for future failure times in a joint type-II censored sample from multiple exponential populations.…”

Section: = ( ) θ λ α βmentioning

confidence: 99%

Bayesian Inference for the Gamma Zero-Truncated Poisson Distribution with an Application to Real Data

Srisuradetchai,

Niyomdecha

2024

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This article presents Bayesian estimation methods applied to the gamma zero-truncated Poisson (GZTP) and the complementary gamma zero-truncated Poisson (CGZTP) distributions, encompassing both one-parameter and two-parameter models. These distributions are notably flexible and useful for modeling lifetime data. In the one-parameter model case, the Jeffreys prior is mathematically derived. The use of informative and noninformative priors, combined with the random walk Metropolis algorithm within a Bayesian framework, generates samples from the posterior distributions. Bayesian estimators’ effectiveness is examined through extensive simulation studies, in comparison with the maximum likelihood method. Results indicate that Bayesian estimators provide more precise parameter estimates, even with smaller sample sizes. Furthermore, the study and comparison of the coverage probabilities (CPs) and average lengths (ALs) of the credible intervals with those from Wald intervals suggest that Bayesian credible intervals typically yield shorter ALs and higher CPs, thereby demonstrating the effectiveness of Bayesian inference in the context of GZTP and CGZTP distributions. Lastly, Bayesian inference is applied to real data.

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Section: = ( ) θ λ α βmentioning

confidence: 99%

Bayesian Inference for the Gamma Zero-Truncated Poisson Distribution with an Application to Real Data

Srisuradetchai,

Niyomdecha

2024

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“…where we choose to use the gamma prior due to its mathematical flexibility and ability to cover a wide range of prior beliefs held by the experimenter; for more details, see Fathi et al [24], Eliwa et al [25], and Dey et al [26]. By combining the LF in (7) and the joint prior distribution (17), the joint posterior distribution is provided by…”

Section: Lf-based Bayesian Estimationmentioning

confidence: 99%

Bayesian Estimation Using Product of Spacing for Modified Kies Exponential Progressively Censored Data

Kurdi,

Nassar,

Alam

2023

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In life testing and reliability studies, most researchers have used the maximum likelihood estimation method to estimate unknown parameters, even though it has been proven that the maximum product of spacing method has properties as good as the maximum likelihood estimation method and sometimes even better. In this study, we aim to estimate the unknown parameters of the modified Kies exponential distribution along with the reliability and hazard rate functions under progressive type-II censoring scheme. The maximum likelihood and maximum product of spacing methods are considered in order to find the point estimates and approximate confidence intervals of the various parameters. Moreover, Bayesian estimations based on the likelihood function and the product of the spacing function of the unknown parameters are obtained using the squared error loss function with independent gamma priors. It is observed that the joint posterior distributions have complicated forms. Because of this, Lindley’s approximation and the Markov chain Monte Carlo technique are used to obtain the Bayesian estimates and highest posterior credible intervals. Monte Carlo simulations are performed in order to evaluate the performance of the proposed estimation methods. Two real datasets are studied to demonstrate the efficacy of the offered methodologies and highlight how simple and applicable it might be to apply them in practical fields.

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General Entropy with Bayes Techniques under Lindley and MCMC for Estimating the New Weibull–Pareto Parameters: Theory and Application

Cited by 2 publications

References 31 publications

Bayesian Inference for the Gamma Zero-Truncated Poisson Distribution with an Application to Real Data

Bayesian Inference for the Gamma Zero-Truncated Poisson Distribution with an Application to Real Data

Bayesian Estimation Using Product of Spacing for Modified Kies Exponential Progressively Censored Data

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