Two-stage and sequential procedures for estimation of powers of parameter of a family of distributions

摘要

For the generalized positive exponential family of distributions, the problems of confidence interval estimation, bounded risk point estimation, and minimum risk point estimation of the rth power of unknown parameter theta are handled. Two-stage and purely sequential methodologies are developed for the estimation purpose. Sequential procedures are developed based on the maximum likelihood estimator (MLE) of the parameter. The exact operating characteristics of these procedures are given.