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Four different estimates of reliability in the exponential case are studied namely the best unbiased, maximum likelihood, Bayes, and the so called naive. Asymptotic normality of the estimators is proved and asymptotic expansions of their expectation and the mean square error are given. Three of these estimators (best unbiased, maximum likelihood, and Bayes) are shown to be efficient and they are studied by using the defficiency concept.
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