Empirical Bayes Estimation for Exponential Model Using Non-parameter  Polynomial Density Estimator

Liu, Manfeng; Ren, Haiping

doi:10.19026/rjaset.5.4964

Cited by 4 publications

(2 citation statements)

References 17 publications

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“…Liu and Ren (2013) [6] study the empirical Bayes estimation of the parameter of the exponential distribution. In the empirical Bayes procedure, they employ the non-parameter polynomial density estimator to the estimation of the unknown marginal probability density function, instead of estimating the unknown prior probability density function of the parameter.…”

Section: Introductionmentioning

confidence: 99%

Comparison Bayes Estimators of Reliability in the Exponential Distribution

ناصر¹

2018

JEAS

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Abstract We produced a study in Estimation for Reliability of the Exponential distribution based on the Bayesian approach. These estimates are derived using Bayesian approaches. In the Bayesian approach, the parameter of the Exponential distribution is assumed to be random variable .we derived bayes estimators of reliability under four types when the prior distribution for the scale parameter of the Exponential distribution is: Inverse Chi-square distribution, Inverted Gamma distribution, improper distribution, Non-informative distribution. And estimators for Reliability is obtained using the well known squared error loss function and weighted squared errors loss function. We used simulation technique, to compare the resultant estimators in terms of their mean squared errors (MSE), mean weighted squared errors (MWSE).Several cases assumed for the parameter of the exponential distribution for data generating, of different samples sizes (small, medium, and large). The results were obtained by using simulation technique, Programs written using MATLAB-R2008a program were used. In general, Simulation results shown that the resultant estimators in terms of their mean squared errors (MSE) is better than the resultant estimators in terms of their mean weighted squared errors (MWSE).According to the our criteria is the best estimator that gives the smallest value of MSE or MWSE . For example bayes estimation is the best when the prior distribution for the scale parameter is improper and Non-informative distributions according to the smallest value of MSE comparative to the values of MWSE for all samples sizes at some of true value of t and .

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Section: Introductionmentioning

confidence: 99%

Comparison Bayes Estimators of Reliability in the Exponential Distribution

ناصر¹

2018

JEAS

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“…Various prior distributions are investigated and the corresponding estimates are derived. Liu and Ren (2013) [6] studied the empirical Bayes estimation of the parameter of the exponential distribution. In the empirical Bayes procedure, they employ the non-parameter polynomial density estimator to the estimation of the unknown marginal probability density function, instead of estimating the unknown prior probability density function of the parameter.…”

Section: Introductionmentioning

confidence: 99%

Comparison of Bayes' Estimators for the Exponential Reliability Function Under Different Prior Functions

Al-obedy¹

2017

IHJPAS

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In this study, we derived the estimation for Reliability of the Exponential distribution based on the Bayesian approach. In the Bayesian approach, the parameter of the Exponential distribution is assumed to be random variable .We derived posterior distribution the parameter of the Exponential distribution under four types priors distributions for the scale parameter of the Exponential distribution is: Inverse Chi-square distribution, Inverted Gamma distribution, improper distribution, Non-informative distribution. And the estimators for Reliability is obtained using the two proposed loss function in this study which is based on the natural logarithm for Reliability function .We used simulation technique, to compare the resultant estimators in terms of their mean squared errors (MSE).Several cases assumed for the parameter of the exponential distribution for data generating of different samples sizes (small, medium, and large). The results were obtained by using simulation technique, Programs written using MATLAB-R2008a program were used. In general, we obtained a good estimations of reliability of the Exponential distribution under the second proposed loss function according to the smallest values of mean squared errors (MSE) for all samples sizes (n) comparative to the estimated values for MSE under the first proposed loss function.

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Maximal entropy prior for the simple step‐stress accelerated test

Moala,

Chagas

2024

Quality & Reliability Eng

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The step‐stress procedure is a popular accelerated test used to analyze the lifetime of highly reliable components. This paper considers a simple step‐stress accelerated test assuming a cumulative exposure model with uncensored lifetime data following a Weibull distribution. The maximum likelihood approach is often used to analyze accelerated stress test data. Another approach is to use the Bayesian inference, which is useful when there is limited data available. In this paper, the parameters of the model are estimated based on the objective Bayesian viewpoint using non‐informative priors. Our main aim is to propose the maximal data information prior (MDIP) presented by Zellner (1984) as an alternative prior to the conventional independent gamma priors for the unknown parameters, in situations where there is little or no a priori knowledge about the parameters. We also obtain the Bayes estimators based on both classes of priors, assuming three different loss functions: square error loss function (SELF), linear‐exponential loss function (LINEX), and generalized entropy loss function (GELF). The proposed MDIP prior is compared with the gamma priors via Monte Carlo simulations by examining their biases and mean square errors under the three loss functions, and coverage probability. Additionally, we employ the Markov Chain Monte Carlo (MCMC) algorithm to extract characteristics of marginal posterior distributions, such as the Bayes estimator and credible intervals. Finally, a real lifetime data is presented to illustrate the proposed methodology.

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Empirical Bayes Estimation for Exponential Model Using Non-parameter Polynomial Density Estimator

Cited by 4 publications

References 17 publications

Comparison Bayes Estimators of Reliability in the Exponential Distribution

Comparison Bayes Estimators of Reliability in the Exponential Distribution

Comparison of Bayes' Estimators for the Exponential Reliability Function Under Different Prior Functions

Maximal entropy prior for the simple step‐stress accelerated test

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