Abstract
This paper deals with Bayesian analysis of two-parameter generalized exponential distribution in proportional hazards model of random censorship. It is well known for two-parameter lifetime distributions that continuous conjugate priors for the parameters do not exist; we assume independent gamma priors for the scale and shape parameter. It is seen that the closed-form expressions for the Bayes estimators cannot be obtained; we suggest Tierney-Kadane’s approximation to obtain the Bayes estimates. However with this method, it is not possible to construct the HPD credible intervals, we propose Gibbs sampling procedure to approximate the Bayes estimates and also to construct the HPD credible intervals. Monte Carlo simulationis carried out to observe the behavior of the proposed methods and to compare with maximum likelihood method. One real data analysis is performed for illustration.
Highlights
Censoring is an important feature of reliability and life-testing experiments
In some medical studies and longitudinal designs, individuals enter into the study simultaneously but the censoring time depends on other random factors, e.g., patients lost to follow-up, drop out of the study, etc
It is to be noted that the noninformative priors for the scale and the shape parameters are the special cases of these independent gamma priors
Summary
Censoring is an important feature of reliability and life-testing experiments. In these experiments the units on test are lost or removed from the test, so that the event of interest may not always be observed for all the units in the study. Friesl and Hurt (20070) dealt with Bayesian estimation in exponential distribution under random censorship model and investigated the asymptotic properties of different estimators with particular stress on the Bayesian risk. The scale and shape parameters of these distributions make them flexible for analyzing any general life time data. Like Weibull and gamma distributions, the GE distribution can have increasing, constant or decreasing hazard function depending on the shape parameter It is observed in Gupta and Kundu (2001) that the GE distribution and the gamma distribution have very similar properties in many respects and in some situations the GE distribution provides a better fit than gamma and Weibull distributions in terms of maximum likelihood or minimum chi-square.
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