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Multistage Estimation of the Scale Parameter of Rayleigh Distribution with Simulation
Open AccessArticle

Multistage Estimation of the Rayleigh Distribution Variance

1
Department of Mathematics, Kuwait College of Science and Technology, KuwaitCity 27235, Kuwait
2
Faculty of Commerce, Menoufia University, Menoufia 32952, Egypt
3
Faculty of Management Sciences, October University for Modern Sciences and Arts, Cairo 11435, Egypt
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(12), 2084; https://doi.org/10.3390/sym12122084
Received: 28 November 2020 / Revised: 14 December 2020 / Accepted: 14 December 2020 / Published: 15 December 2020
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. View Full-Text
Keywords: asymptotic regret; coverage probability; loss function; Monte Carlo simulation; optimal stopping rule; three-stage procedure asymptotic regret; coverage probability; loss function; Monte Carlo simulation; optimal stopping rule; three-stage procedure
MDPI and ACS Style

Yousef, A.; Amin, A.A.; Hassan, E.E.; Hamdy, H.I. Multistage Estimation of the Rayleigh Distribution Variance. Symmetry 2020, 12, 2084. https://doi.org/10.3390/sym12122084

AMA Style

Yousef A, Amin AA, Hassan EE, Hamdy HI. Multistage Estimation of the Rayleigh Distribution Variance. Symmetry. 2020; 12(12):2084. https://doi.org/10.3390/sym12122084

Chicago/Turabian Style

Yousef, Ali; Amin, Ayman A.; Hassan, Emad E.; Hamdy, Hosny I. 2020. "Multistage Estimation of the Rayleigh Distribution Variance" Symmetry 12, no. 12: 2084. https://doi.org/10.3390/sym12122084

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