The estimation of survivor functions from several independent exponential models based on differing sample sizes is developed. It is investigated whether or not all the samples are from the same population and this information is used to improve upon the usual estimates of the survival function. Thus estimators presented are based on the James#x2013;Stein and preliminary test rules. It is demonstrated that James#x2013;Stein type estimators are superior to the classical estimators. However, it is also indicated through asymptotic and simulation results that none of the preliminary test and shrinkage estimators dominate each other though they perform well relative to the usual estimators. The relative dominance picture of the estimators is presented.
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