Fixed width confidence interval for the parameter of U (aθ, bθ) distribution

2019 ◽  
Vol 38e (2) ◽  
pp. 511
Author(s):  
V.N. Kadam ◽  
H.S. Patil
Keyword(s):  
Confidence Interval ◽  
Width Confidence Interval

scholarly journals Multistage Estimation of the Rayleigh Distribution Variance

Symmetry ◽  
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.

Fixed Length Interval Estimation of the Location Parameter of a Pareto Distribution

1986 ◽  
Vol 35 (1-2) ◽  
pp. 67-76 ◽  
Author(s):  
Malay Ghosh ◽  
Dennis Wackerly
Keyword(s):  
Confidence Interval ◽  
Shape Parameter ◽  
Pareto Distribution ◽  
Interval Estimation ◽  
Location Parameter ◽  
Fixed Length ◽  
Asymptotically Efficient ◽  
Width Confidence Interval

A sequential fixed-width confidence interval for the location parameter of a Pareto distribution with unknown shape parameter is developed. The procedure Is shown to be asymptotically consistent and asymptotically efficient in the sense of Chow and Robbins (1965).

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