Multistage Estimation of the Rayleigh Distribution Variance

Abstract

In this paper we discuss the multistage sequential estimation of the variance of the Rayleigh distribution using the three-stage procedure that was presented by Hall (Ann. Stat. 9(6):1229–1238, 1981). Since the Rayleigh distribution variance is a linear function of the distribution scale parameter’s square, it suffices to estimate the Rayleigh distribution’s scale parameter’s square. We tackle two estimation problems: first, the minimum risk point estimation problem under a squared-error loss function plus linear sampling cost, and the second is a fixed-width confidence interval estimation, using a unified optimal stopping rule. Such an estimation cannot be performed using fixed-width classical procedures due to the non-existence of a fixed sample size that simultaneously achieves both estimation problems. We find all the asymptotic results that enhanced finding the three-stage regret as well as the three-stage fixed-width confidence interval for the desired parameter. The procedure attains asymptotic second-order efficiency and asymptotic consistency. A series of Monte Carlo simulations were conducted to study the procedure’s performance as the optimal sample size increases. We found that the simulation results agree with the asymptotic results.

Triple Sampling Inference Procedures for the Mean of the Normal Distribution When the Population Coefficient of Variation Is Known

“…Yousef [39,40] tackled estimation of the normal inverse coefficient of variation using Monte Carlo simulation. For other underlying distributions, see Yousef et al [41,42]. For triple sampling minimum risk point estimation for a function of a normal mean under weighted power absolute error loss plus cost, see Banerjee and Mukhopadhyay [43].…”