Bayes estimation of Gompertz distribution parameters and acceleration factor under partially accelerated life tests with type-I censoring

İsmail, Ali A.

doi:10.1080/00949650903045058

Cited by 52 publications

(24 citation statements)

References 25 publications

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“…It is not possible to compute (22) analytically, therefore, we propose to approximate (22) by using MCMC technique to generate samples from the posterior distributions and then compute the Bayes estimators of the individual parameters.…”

Section: Bayes Estimation Based On Bsel Functionmentioning

confidence: 99%

“…[4] considered the Bayesian estimates of the parameters, reliability and hazard rate functions by using an approximate form due to Tierney and Kadane of a mixtures of two Weibull components under ALT. Finally, [22] obtained the Bayesian estimation of Gompertz distribution parameters in the case of step-stress PALT with two stress levels and Type-I censoring and the approximation Bayes estimates are computed using the method of Lindley.…”

Section: Introductionmentioning

confidence: 99%

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Inference on Constant-Partially Accelerated Life Tests for Mixture of Pareto Distributions under Progressive Type-II Censoring

Abushal¹,

AL-Zaydi²

2017

OJS

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The main purpose of this paper is to obtain the inference of parameters of heterogeneous population represented by finite mixture of two Pareto (MTP) distributions of the second kind. The constant-partially accelerated life tests are applied based on progressively type-II censored samples. The maximum likelihood estimates (MLEs) for the considered parameters are obtained by solving the likelihood equations of the model parameters numerically. The Bayes estimators are obtained by using Markov chain Monte Carlo algorithm under the balanced squared error loss function. Based on Monte Carlo simulation, Bayes estimators are compared with their corresponding maximum likelihood estimators. The two-sample prediction technique is considered to derive Bayesian prediction bounds for future order statistics based on progressively type-II censored informative samples obtained from constant-partially accelerated life testing models. The informative and future samples are assumed to be obtained from the same population. The coverage probabilities and the average interval lengths of the confidence intervals are computed via a Monte Carlo simulation to investigate the procedure of the prediction intervals. Analysis of a simulated data set has also been presented for illustrative purposes. Finally, comparisons are made between Bayesian and maximum likelihood estimators via a Monte Carlo simulation study.

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Section: Bayes Estimation Based On Bsel Functionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Inference on Constant-Partially Accelerated Life Tests for Mixture of Pareto Distributions under Progressive Type-II Censoring

Abushal¹,

AL-Zaydi²

2017

OJS

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“…Abdel-Ghani [3] considered the Bayesian approach to estimate the parameters of Weibull distribution in SSPALT with censoring. Ismail [20] considered the Bayesian approach to estimate the parameters of Gompertz distribution with time-censoring.…”

Section: Introductionmentioning

confidence: 99%

Likelihood and Bayesian estimations for step-stress life test model under Type-I censoring

İsmail¹

2014

HJMS

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This paper discusses likelihood and Bayesian estimations for partially accelerated step-stress life test model under Type-I censoring assuming Pareto distribution of the second kind. The posterior means and posterior variances are obtained under the squared error loss function using Lindleys approximation procedure. It has been observed that Lindley's method usually provides posterior variances and mean square errors smaller than those of the maximum likelihood estimators. Furthermore, the highest posterior density credible intervals of the model parameters based on Gibbs sampling technique are computed. For illustration, simulation studies and an illustrative example based on a real data set are provided.

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“…Recently, Aly and Ismail (2008) studied the optimal design problem of step-stress PALT in the case of Weibull distribution with type-I censored data. More recently, Ismail (2010) applied the Bayesian approach to the estimation problem in the case of step stress partially accelerated life tests with two stress levels and type-I censoring assuming the two-parameter Gompertz distribution as a lifetime model. This paper concentrates on both estimation and optimal design problems in the case of the two-parameter Gompertz distribution under step-stress PALT using type-II censored data.…”

Section: Introductionmentioning

confidence: 99%

Planning step-stress life tests with type-ii censored data

İsmail¹

2011

Sci. Res. Essays

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This study discusses the point and interval estimations of two-parameter Gompertz distribution under partially accelerated life tests with Type-II censoring. Also, the study considers the optimal design problem in the case of time step-stress model. The maximum likelihood estimators and approximate confidence intervals of the model parameters are derived. Also, optimum test plans for the time stepstress life tests are developed. For illustration, a simulation study is provided.

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Bayes estimation of Gompertz distribution parameters and acceleration factor under partially accelerated life tests with type-I censoring

Cited by 52 publications

References 25 publications

Inference on Constant-Partially Accelerated Life Tests for Mixture of Pareto Distributions under Progressive Type-II Censoring

Inference on Constant-Partially Accelerated Life Tests for Mixture of Pareto Distributions under Progressive Type-II Censoring

Likelihood and Bayesian estimations for step-stress life test model under Type-I censoring

Planning step-stress life tests with type-ii censored data

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