Abstract
This paper provides the Bayes estimators of scale parameters in two exponential distributions mixed in proportion p, which is assumed to be known. For deriving the Bayes estimators the prior distributions are chosen such that they are centered at the known prior values of the scale parameters. The Bayes estimators thus obtained are found to be equivalent to Thompson's shrinkage estimators. The Bayes estimator of reliability function and another estimator of reliability using the Bayes estimators of scale parameters are given. The efficiency of the proposed estimator of reliability with respect to its maximum likelihood estimator (mle) is studied by Monte Carlo simulation. Lastly, the Bayes confidence interval of reliability is obtained and its validity is examined by a Monte Carlo study of 500 samples.
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