Large Second-Order Properties of a Two-Stage Point Estimation Procedure for the Range in a Power Family Distribution

In this article, a new two-stage sampling methodology is explored for the minimum risk point estimation of the range θ in a power family distribution. This modification of Mukhopadhyay et al.'s (1983) twostage estimation technique is proposed along the lines of Mukhopadhyay and Duggan (1997, 1999) by assuming a prior knowledge of a positive lower bound θ_L for the otherwise unknown range parameter θ. Expressions for the average sample size and the risk associated with the conventional sample maximum order statistic are investigated. A new estimator of 8 based only on the stopping variable is also investigated. Various second-order asymptotic analyses are supplemented by interesting exact and simulation results.