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.

scholarly journals Three-Stage Sequential Estimation of the Inverse Coefficient of Variation of the Normal Distribution

Computation ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 69 ◽  
Author(s):  
Ali Yousef ◽  
Hosny Hamdy
Keyword(s):  
Confidence Interval ◽  
Normal Distribution ◽  
Coefficient Of Variation ◽  
Sequential Estimation ◽  
Point Estimation ◽  
Squared Error Loss Function ◽  
Fixed Sample ◽  
Sampling Cost ◽  
Better Than ◽  
Inverse Coefficient

This paper sequentially estimates the inverse coefficient of variation of the normal distribution using Hall’s three-stage procedure. We find theorems that facilitate finding a confidence interval for the inverse coefficient of variation that has pre-determined width and coverage probability. We also discuss the sensitivity of the constructed confidence interval to detect a possible shift in the inverse coefficient of variation. Finally, we find the asymptotic regret encountered in point estimation of the inverse coefficient of variation under the squared-error loss function with linear sampling cost. The asymptotic regret provides negative values, which indicate that the three-stage sampling does better than the optimal fixed sample size had the population inverse coefficient of variation been known.

scholarly journals Multistage Estimation of the Scale Parameter of Rayleigh Distribution with Simulation

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1925 ◽  
Author(s):  
Ali Yousef ◽  
Emad E. H. Hassan ◽  
Ayman A. Amin ◽  
Hosny I. Hamdy
Keyword(s):  
Confidence Interval ◽  
Scale Parameter ◽  
Sequential Sampling ◽  
Interval Estimation ◽  
Rayleigh Distribution ◽  
Sampling Procedure ◽  
Optimal Decision ◽  
Large Sample Size ◽  
Asymptotic Results ◽  
Confidence Interval Estimation

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.

scholarly journals Survival estimation for singly type one censored sample based on generalized Rayleigh distribution

2014 ◽  
Vol 11 (2) ◽  
pp. 193-201
Author(s):  
Baghdad Science Journal
Keyword(s):  
Current Model ◽  
Survival Function ◽  
Information Matrix ◽  
Interval Estimation ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Point Estimation ◽  
Distribution Model ◽  
Unknown Parameters ◽  
Generalized Rayleigh Distribution

This paper interest to estimation the unknown parameters for generalized Rayleigh distribution model based on censored samples of singly type one . In this paper the probability density function for generalized Rayleigh is defined with its properties . The maximum likelihood estimator method is used to derive the point estimation for all unknown parameters based on iterative method , as Newton – Raphson method , then derive confidence interval estimation which based on Fisher information matrix . Finally , testing whether the current model ( GRD ) fits to a set of real data , then compute the survival function and hazard function for this real data.

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).

Asymptotical problems of sequential interval and point estimation

2020 ◽  
Vol 86 (7) ◽  
pp. 72-80
Author(s):  
A. A. Abdushukurov ◽  
G. G. Rakhimova
Keyword(s):  
Distribution Function ◽  
Confidence Intervals ◽  
Wide Class ◽  
Sequential Analysis ◽  
Interval Estimation ◽  
Sequential Estimation ◽  
Point Estimation ◽  
Minimum Risk ◽  
Unknown Distribution ◽  
Unknown Distribution Function

The accuracy of interval estimation systems is usually measured using interval lengths for given covering probabilities. The confidence intervals are the intervals of a fixed width if the length of the interval is determined, i.e., not random, and tends to zero for a given covering probability. We consider two important directions of statistical analysis -sequential interval estimation with confidence intervals of fixed width and sequential point estimation with asymptotically minimum risk. Two statistical models are used to describe the basis problems of sequential interval estimation by confidence intervals of a fixed width and point estimation. A review of data on nonparametric sequential estimation is carried out and new original results obtained by the authors are presented. Sequential analysis is characterized by the fact that the moment of termination of observations (stopping time) is random and is determined depending on the values of the observed data and on the adopted measure of optimality of the constructed statistical estimate. Therefore, to solve the asymptotic problems of sequential estimation, the methods of summation of random variables are used. To prove the asymptotic consistency of the confidence intervals of a fixed width, we used a method based on application of limit theorems for randomly stopped random processes. General conditions of the consistency and efficiency of sequential interval estimation of a wide class of functionals of an unknown distribution function are obtained and verified by sequential interval estimation of an unknown probability density of asymptotically uncorrelated and linear processes. Conditions of the regularity are specified that provide the property of being an estimate with an asymptotically minimum risk for a wide class of estimates and loss functions. Those conditions are verified by sequential point estimation of an unknown distribution function.

Sampling for Confidence Interval Estimation of the Fiber Shape Factor

1980 ◽  
Vol 102 (4) ◽  
pp. 366-368
Author(s):  
C. B. Russell ◽  
R. L. Barker ◽  
D. W. Lyons
Keyword(s):  
Confidence Interval ◽  
Sample Size ◽  
Uniform Distribution ◽  
Shape Factor ◽  
Interval Estimation ◽  
Sampling Plan ◽  
Cotton Fibers ◽  
Longitudinal View ◽  
Confidence Interval Estimation ◽  
Adequate Sample Size

A method is described for estimating the shape factor, the ratio of the maximum and minimum projected diameters, of a fiber from measurements made on a longitudinal view. The method assumes that the measured diameters have a uniform distribution, an assumption which seems justified for cotton fibers. An estimator of the shape factor is given; a confidence interval for the shape factor is derived; and a sampling plan together with formulae for determining an adequate sample size is presented.

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