Multistage Estimation of the Scale Parameter of Rayleigh Distribution with Simulation

Abstract

This paper discusses the sequential estimation of the scale parameter of the Rayleigh distribution using the three‐stage sequential sampling procedure proposed by Hall (Ann. Stat. 1981, 9, 1229–1238). Both point and confidence interval estimation are considered via a unified optimal decision framework, which enables one to make the maximum use of the available data and, at the same time, reduces the number of sampling operations by using bulk samples. The asymptotic characteristics of the proposed sampling procedure are fully discussed for both point and confidence interval estimation. Since the results are asymptotic, Monte Carlo simulation studies are conducted to provide the feel of small, moderate, and large sample size performance in typical situations using the Microsoft Developer Studio software. The procedure enjoys several interesting asymptotic characteristics illustrated by the asymptotic results and supported by simulation.