Classical and Bayesian estimation of stress-strength reliability in type II censored Pareto distributions

Abravesh, Akbar; Ganji, Masoud; Mostafaiy, Behdad

doi:10.1080/03610918.2018.1457688

Cited by 5 publications

(7 citation statements)

References 22 publications

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“…Abravesh et al [4] showed that Equations (43) and ( 45) have no answer and set α 1 = α 2 = 1 to solve this problem. Then, η 1 = b 1 ′/r 1 and η 2 = b 2 ′/r 2 .…”

Section: Conjugate Informativementioning

confidence: 99%

“…Qixuan and Wenhao [3] worked on the Bayesian and classical estimation of stress-strength reliability for inverse Weibull lifetime models. Abravesh et al [4] obtained classical and Bayesian estimation of stress-strength reliability in type II censored Pareto distributions. Akgül et al [5] presented inferences on stress-strength reliability based on ranked set sampling data in the case of Lindley distribution.…”

Section: Introductionmentioning

confidence: 99%

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Statistical Inference of Stress-Strength Reliability of Gompertz Distribution under Type II Censoring

Ezmareh

Yari

2022

Advances in Mathematical Physics

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This paper develops the problem of estimating stress-strength reliability for Gompertz lifetime distribution. First, the maximum likelihood estimation (MLE) and exact and asymptotic confidence intervals for stress-strength reliability are obtained. Then, Bayes estimators under informative and noninformative prior distributions are obtained by using Lindley approximation, Monte Carlo integration, and MCMC. Bayesian credible intervals are constructed under these prior distributions. Also, simulation studies are used to illustrate these inference methods. Finally, a real dataset is analyzed to show the implementation of the proposed methodologies.

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“…Abravesh et al [4] showed that Equations (43) and ( 45) have no answer and set α 1 = α 2 = 1 to solve this problem. Then, η 1 = b 1 ′/r 1 and η 2 = b 2 ′/r 2 .…”

Section: Conjugate Informativementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Statistical Inference of Stress-Strength Reliability of Gompertz Distribution under Type II Censoring

Ezmareh

Yari

2022

Advances in Mathematical Physics

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“…Next as described in Wong [22] and Abravesh et al [23] we obtain the asymptotic distribution ofR and is given in the following theorem.…”

Section: Asymptotic Distribution Ofrmentioning

confidence: 99%

Inference on P(Y<X) Based on Record Values for Generalized Pareto Distribution

Chacko

Mathew²

2020

Calcutta Statistical Association Bulletin

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In this article, the estimation of [Formula: see text] is considered when [Formula: see text] and [Formula: see text] are two independent generalized Pareto distributions. The maximum likelihood estimators and Bayes estimators of [Formula: see text] are obtained based on record values. The Asymptotic distributions are also obtained together with the corresponding confidence interval of [Formula: see text]. AMS 2000 subject classification: 90B25

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“…Reference [9] studied the confdence interval estimation and approximate hypothesis testing for the reliability of the Pareto distribution based on progressively type-II-censored data with the generalized variable method. Reference [10] assumed the scale parameter of the Pareto distribution to be known and obtained the Bayesian reliability estimate using conjugate and Jefrey's priors based on type-II-censored data. Reference [11], with the generalized variable method, investigated the reliability of the generalized Pareto distribution.…”

Section: Introductionmentioning

confidence: 99%

“…Reference [18] studied the analysis of stress-strength reliability model based on the Pareto distribution using records, and [10] studied this model based on censored data. However, an analysis of the stress-strength reliability model for the Pareto distribution based on GOS is not available in the statistical literature.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Estimation of the Stress-Strength Reliability Based on Generalized Order Statistics for Pareto Distribution

Ezmareh,

Yari

2023

Journal of Probability and Statistics

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The aim of this paper is to obtain a Bayesian estimator of stress-strength reliability based on generalized order statistics for Pareto distribution. The dependence of the Pareto distribution support on the parameter complicates the calculations. Hence, in literature, one of the parameters is assumed to be known. In this paper, for the first time, two parameters of Pareto distribution are considered unknown. In computing the Bayesian confidence interval for reliability based on generalized order statistics, the posterior distribution has a complex form that cannot be sampled by conventional methods. To solve this problem, we propose an acceptance-rejection algorithm to generate a sample of the posterior distribution. We also propose a particular case of this model and obtain the classical and Bayesian estimators for this particular case. In this case, to obtain the Bayesian estimator of stress-strength reliability, we propose a variable change method. Then, these confidence intervals are compared by simulation. Finally, a practical example of this study is provided.

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Classical and Bayesian estimation of stress-strength reliability in type II censored Pareto distributions

Cited by 5 publications

References 22 publications

Statistical Inference of Stress-Strength Reliability of Gompertz Distribution under Type II Censoring

Statistical Inference of Stress-Strength Reliability of Gompertz Distribution under Type II Censoring

Inference on P(Y<X) Based on Record Values for Generalized Pareto Distribution

Bayesian Estimation of the Stress-Strength Reliability Based on Generalized Order Statistics for Pareto Distribution

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