Bounded Risk Two-stage Estimation Procedure for a U(aθ, bθ) Distribution

Abstract

In the literature, an extensive work on sequential fixed-width confidence interval for the parameter of U( q, m q) model, where m > 1 is known, is available. In this article, we propose a two-stage sampling procedure for estimating the parameter q of U( aq, bq) distribution, where a < b are positive and known. Here, the risk of an estimator [Formula: see text] of q is less than a pre-assigned number w (>0), that is, [Formula: see text], 0 < A < ∞ is known. We determine the parameter Bk of stopping variable so that the risk is uniformly bounded by a pre-assigned value w. We have also tabulated the values of the expected stopping time and its standard deviation (SD).