Multistage Estimation of the Scale Parameter of Rayleigh Distribution with Simulation

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.

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Multistage Estimation of the Rayleigh Distribution Variance

Symmetry ◽

10.3390/sym12122084 ◽

2020 ◽

Vol 12 (12) ◽

pp. 2084

Author(s):

Ali Yousef ◽

Ayman A. Amin ◽

Emad E. Hassan ◽

Hosny I. Hamdy

Keyword(s):

Confidence Interval ◽

Sample Size ◽

Interval Estimation ◽

Sequential Estimation ◽

Rayleigh Distribution ◽

Point Estimation ◽

Asymptotic Results ◽

Squared Error Loss Function ◽

Estimation Problems ◽

Width Confidence Interval

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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FixedWidth Confidence Interval of P(X < Y) under a Data Dependent Adaptive Allocation Design

Austrian Journal of Statistics ◽

10.17713/ajs.v36i3.330 ◽

2016 ◽

Vol 36 (3) ◽

Author(s):

Uttam Bandyopadhyay ◽

Radhakanta Das

Keyword(s):

Confidence Interval ◽

Present Article ◽

Continuous Distribution ◽

Interval Estimation ◽

Estimation Procedure ◽

Distribution Functions ◽

Adaptive Procedure ◽

Asymptotic Results ◽

Adaptive Allocation ◽

Confidence Interval Estimation

The present article is related to a nonparametric fixed-width confidence interval estimation of the parameter µ = P(X < Y ) = R F(y)dG(y), where F and G are two unknown continuous distribution functions. The estimation procedure is based on a sample obtained under some non-iid adaptive situation. We provide various asymptotic results related to the proposed procedure and compare it with a non-adaptive procedure.

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