Abstract
This paper develops Bayesian estimation and prediction, for a mixture of Weibull and Lomax distributions, in the context of the new life test plan called progressive first failure censored samples. Maximum likelihood estimation and Bayes estimation, under informative and non-informative priors, are obtained using Markov Chain Monte Carlo methods, based on the symmetric square error Loss function and the asymmetric linear exponential (LINEX) and general entropy loss functions. The maximum likelihood estimates and the different Bayes estimates are compared via a Monte Carlo simulation study. Finally, Bayesian prediction intervals for future observations are obtained using a numerical example
Highlights
Mixtures models have received great attention from analysts in the recent years due to their important role in life testing and reliability
Attention has been paid by some authors to the finite mixtures to discuss lifetime distributions, [see Everitt and Hand (1981),Titterington et al (1985), Mclachlan and Basford (1988), Lindsay (1995), Mclachlan and Peel (2000)]
The Weibull distribution has been widely used in modeling of lifetime event data; this is due to the variety of shapes of the probability density function based on its parameters
Summary
Mixtures models have received great attention from analysts in the recent years due to their important role in life testing and reliability. The Weibull distribution has been widely used in modeling of lifetime event data; this is due to the variety of shapes of the probability density function (pdf) based on its parameters. Conventional censoring scheme can shorten the duration of a life test, the experimental time is still too long that cannot be waited for when the units are highly reliable. The prediction problems of the future samples based on censored data is an important topic in statistics. The objective of this work is to apply the Bayesian procedure to estimate the parameters and obtain two sample prediction bounds for future observations from the proposed model, based on progressive first failure censoring scheme. The rest of this paper is organized as follows: In Section 2, the progressive first-failure censoring scheme is described.
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