Estimation of scale parameters for two exponential distributions [reliability theory]

The scale parameter of the exponential distribution is estimated using conditional specification. When there are two censored samples available for estimating the scale parameter, a preliminary test is usually used to determine whether to pool the samples or to use the individual minimum-variance unbiased estimator. This latter estimator (usual preliminary-test estimator) is studied. The optimum levels of significance and their corresponding critical values for the preliminary test are obtained on the basis of the minimax regret criterion. A preliminary-test shrinkage estimator is proposed, and the optimum values of its shrinkage estimator is proposed, and the optimum values of its shrinkage coefficients are obtained. For a mean-square-error criterion of goodness of estimation, the preliminary-test shrinkage estimator is better than the usual preliminary-test estimator