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Article

Multistage Estimation of the Scale Parameter of Rayleigh Distribution with Simulation

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Department of Mathematics, Faculty of Engineering, Kuwait College of Science and Technology, Doha District POBox 27235, Kuwait
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Faculty of Management Sciences, October University for Modern Sciences and Arts, 6th October City, 12566 Cairo, Egypt
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Faculty of Commerce, Menoufia University, Gamal Abd El-Nasir, Qism Shebeen El-Kom, Shibin el Kom, Menofia Governorate, Menoufia, Egypt
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(11), 1925; https://doi.org/10.3390/sym12111925
Received: 3 November 2020 / Revised: 18 November 2020 / Accepted: 20 November 2020 / Published: 22 November 2020
This paper discusses the sequential estimation of the scale parameter of the Rayleigh distribution using the three-stage sequential sampling procedure proposed by Hall (Ann. Stat.1981, 9, 1229–1238). Both point and confidence interval estimation are considered via a unified optimal decision framework, which enables one to make the maximum use of the available data and, at the same time, reduces the number of sampling operations by using bulk samples. The asymptotic characteristics of the proposed sampling procedure are fully discussed for both point and confidence interval estimation. Since the results are asymptotic, Monte Carlo simulation studies are conducted to provide the feel of small, moderate, and large sample size performance in typical situations using the Microsoft Developer Studio software. The procedure enjoys several interesting asymptotic characteristics illustrated by the asymptotic results and supported by simulation. View Full-Text
Keywords: asymptotic regret; coverage probability; loss function; three-stage procedure asymptotic regret; coverage probability; loss function; three-stage procedure
MDPI and ACS Style

Yousef, A.; Hassan, E.E.H.; Amin, A.A.; Hamdy, H.I. Multistage Estimation of the Scale Parameter of Rayleigh Distribution with Simulation. Symmetry 2020, 12, 1925. https://doi.org/10.3390/sym12111925

AMA Style

Yousef A, Hassan EEH, Amin AA, Hamdy HI. Multistage Estimation of the Scale Parameter of Rayleigh Distribution with Simulation. Symmetry. 2020; 12(11):1925. https://doi.org/10.3390/sym12111925

Chicago/Turabian Style

Yousef, Ali, Emad E.H. Hassan, Ayman A. Amin, and Hosny I. Hamdy 2020. "Multistage Estimation of the Scale Parameter of Rayleigh Distribution with Simulation" Symmetry 12, no. 11: 1925. https://doi.org/10.3390/sym12111925

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