Multistage Estimation of the Scale Parameter of Rayleigh Distribution with Simulation

Yousef, Ali; Hassan, Emad E. H.; Amin, Ayman A.; Hamdy, H. I.

doi:10.3390/sym12111925

Cited by 3 publications

(1 citation statement)

References 48 publications

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“…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].…”

Section: Sequential Sampling Proceduresmentioning

confidence: 99%

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

2023

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This paper discusses the triple sampling inference procedures for the mean of a symmetric distribution—the normal distribution when the coefficient of variation is known. We use the Searls’ estimator as an initial estimate for the unknown population mean rather than the classical sample mean. In statistics literature, the normal distribution under investigation underlines almost all the natural phenomena with applications in many fields. First, we discuss the minimum risk point estimation problem under a squared error loss function with linear sampling cost. We obtained all asymptotic results that enhanced finding the second-order asymptotic risk and regret. Second, we construct a fixed-width confidence interval for the mean that satisfies at least a predetermined nominal value and find the second-order asymptotic coverage probability. Both estimation problems are performed under a unified optimal framework. The theoretical results reveal that the performance of the triple sampling procedure depends on the numerical value of the coefficient of variation—the smaller the coefficient of variation, the better the performance of the procedure.

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Section: Sequential Sampling Proceduresmentioning

confidence: 99%

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

2023

Self Cite

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Multistage Estimation of the Rayleigh Distribution Variance

et al. 2020

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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.

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Editorial of the Special Issue “Skewed (Asymmetrical) Probability Distributions and Applications across Disciplines”

Castro-Palacio

Córdoba

2023

Symmetry

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Multistage Estimation of the Scale Parameter of Rayleigh Distribution with Simulation

Cited by 3 publications

References 48 publications

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

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

Multistage Estimation of the Rayleigh Distribution Variance

Editorial of the Special Issue “Skewed (Asymmetrical) Probability Distributions and Applications across Disciplines”

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