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.
Highlights
Let X1, X2, . . . be a sequence of independent and identically distributed random variables from a normal distribution N μ, σ 2 with mean μ∈ R and variance σ 2 ∈ R+, both parameters are finite but unknown
The results showed that the three-stage procedure attains asymptotic efficiency and consistency in the sense of Chow and Robbins [18]
We examine the performance of the three-stage procedure for estimating the population inverse coefficient of variation of the normal distribution
Summary
Let X1, X2, . . . be a sequence of independent and identically distributed random variables from a normal distribution N μ, σ 2 with mean μ∈ R and variance σ 2 ∈ R+, both parameters are finite but unknown. The higher the coefficient of variation, the greater the level of dispersion around the mean. It is a unit-free measure that allows for comparison between distributions of values whose scales of measurement are not comparable. Hima Bindu et al [3] published a book, which provides necessary exposure of computational strategies, properties of the coefficient of variation, and extracting the metadata leading to efficient knowledge representation. It compiles representational and classification strategies based on the measure through illustrative explanations. We recommend to work with the reciprocal of the measure, inverse coefficient of variation, that is η
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