A Sequential Estimation Procedure for the Parameter of an Exponential Distribution

Abstract

A Bayesian sequential estimation problem for the parameter # of n exponentially distributed random variables £1, is considered. If observation is stopped at time t9a 1.(41,0, At, cr(i At, 1 (int))-Pleasurable estimator 79.t has to be used, and the loss is given by (#t — #)2-faNo(t) 4-bt, where NQ(t) is the number of A; which are t. A postal interpretation is that the statistician simultaneously observes n “individuals” and has to estimate sequentially the parameter of their common lifetime distribution, where at time i the number of individuals having died so far and their death dates are known. For a gamma prior distribution of P the optimal stopping time and the bayes risk is found. © 1990, Taylor & Francis Group, LLC. All rights reserved.