Three-Stage Sequential Estimation of the Inverse Coefficient of Variation of the Normal Distribution

Abstract

This paper sequentially estimates the inverse coefficient of variation of the normal distribution using Hall’s three-stage procedure. We find theorems that facilitate finding a confidence interval for the inverse coefficient of variation that has pre-determined width and coverage probability. We also discuss the sensitivity of the constructed confidence interval to detect a possible shift in the inverse coefficient of variation. Finally, we find the asymptotic regret encountered in point estimation of the inverse coefficient of variation under the squared-error loss function with linear sampling cost. The asymptotic regret provides negative values, which indicate that the three-stage sampling does better than the optimal fixed sample size had the population inverse coefficient of variation been known.

Performance of Three-Stage Sequential Estimation of the Normal Inverse Coefficient of Variation Under Type II Error Probability: A Monte Carlo Simulation Study

“…In this paper, we continue the research of estimating the population inverse coefficient of variation of the normal distribution by examining the performance of the procedure under (3) and verify the theoretical results found by Yousef and Hamdy [11] under moderate sample sizes. We estimate all the parameters in concern; the final sample size N, the population, mean µ, the population variance σ 2 , and the population inverse coefficient of variation η.…”

“…That is the half-width of the interval is d, and the coverage probability is at least 100 (1 − α ) %. It was shown from Yousef and Hamdy [11] Corollary 2 parts…”

“…The results showed that the three-stage procedure attains asymptotic efficiency and consistency in the sense of Chow and Robbins [18]. Recently, Yousef and Hamdy [11] reconsidered the same problem but theoretically using an optimal sample size of the form,…”

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

“…Both Son et al [36] and Yousef [35,38] provided second-order approximations of the characteristic operating function of the inference. 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].…”

Multistage Estimation of the Scale Parameter of Rayleigh Distribution with Simulation

“…Others have tried to improve the inference quality by protecting the inference against type II error probability, studying the characteristic operating curve, or/and discussing three-stage sampling's sensitivity when the underlying distribution departs from normality. For more details, see Mukhopadhyay [37][38][39], Mukhopadhyay et al [40], Mukhopadhyay and Mauromoustakos [41], Hamdy and Palotta [42], Hamdy et al [43], Hamdy [28], Hamdy et al [44], Mukhopadhyay and Padmanabhan [45], Takada [46], Hamdy [47], Al-Mahmeed and Hamdy [48], AlMahmeed et al [49], Costanzo et al [50], Yousef et al [51], Yousef [52], Hamdy et al [53], Yousef [54], Yousef and Hamdy [55,56], and Yousef [57].…”