SEQUENTIAL POINT ESTIMATION PROCEDURES FOR THE GENERALIZED LIFE DISTRIBUTIONS
Keywords:
Generalized Life Distributions, Sequential Estimation, Regret, Second-order Approximations, Improved Estimator.Abstract
The problem of minimum risk point estimation under squared-error loss function (SELF) for the parameter associated with the generalized life distributions, is considered. The failure of fixed sample size procedure is established. Sequential procedure using uniformly minimum variance unbiased estimator (UMVUE) at both the stopping and estimation stages is developed and the second-order approximations are derived. The regret of the sequential procedure is obtained and the condition under which the regret may be negative is discussed. Finally, an improved estimator is proposed and its dominance over the UMVUE (in terms of having smaller risk) is also established .
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