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

Abstract

This paper sheds light on the performance of the three-stage sequential estimation of the population inverse coefficient of variation of the normal distribution under a moderate sample size. We estimate the final sample size generated by the three-stage procedure, and the population mean, the population variance, the population inverse coefficient of variation, the asymptotic coverage probability, and the asymptotic regret incurred by estimating the population inverse coefficient of variation by its sample statistics under squared-error loss function plus linear sampling cost. Besides, we address the sensitivity of the constructed confidence interval to detect a potential shift that may occur in the population inverse coefficient of variation under uncontrolled and controlled optimal sample size against type II error probability. We do so by computing the characteristic operating function. Besides, we address the sensitivity of the three-stage procedure as the underlying distribution departs away from normality. We consider two classes of distributions: Student's t distribution and beta distribution. We use Monte Carlo simulations for this study. We write FORTRAN codes and use Microsoft developer studio software. The simulation results revealed that the controlled confidence intervals provide coverage probabilities that exceed the prescribed nominal value even for small optimal sample size contrary to the uncontrolled case that attains the nominal value only asymptotically. Moreover, under the controlled case, the sensitivity of the procedure to depict a potential shift in the parameter of concern becomes more sensitive than the uncontrolled case. Finally, the three-stage procedure is non-sensitive to departure from normality for normal likewise distributions.

Probabilistic creep with the Wilshire–Cano–Stewart model

“…The coefficient of variation (CoV) convergence test is performed to determine the required number of MCMC run as shown in Figure 6. 59,60 The CoV of MCSR and SR exhibits convergence after around 700 samples. On the contrary, the CoV of ductility is observed to be converging after 200 samples.…”

“…In this study, the initial 500 samples are regarded as “warm‐up” samples. The coefficient of variation (CoV) convergence test is performed to determine the required number of MCMC run as shown in Figure 6 59,60 . The CoV of MCSR and SR exhibits convergence after around 700 samples.…”

Features of the coefficient of variation of parameters of the gas environment in fire in the premises

“…The application of the coefficient of variation in hydrology is discussed in [29]. A three-step method for estimating the coefficient of variation is proposed in [30]. However, the proposed method is limited to estimating the inverse coefficient of variation and studying the second type error using the Monte Carlo procedure.…”

“…However, the proposed method is limited to estimating the inverse coefficient of variation and studying the second type error using the Monte Carlo procedure. Thus, despite the noted wide possibilities of the coefficient of variation, in [26][27][28][29][30] there are no studies of the features of the coefficient of variation of the DHP GE characteristic of the initial stage of CM.…”

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].…”