scholarly journals Estimation of the Rayleigh Distribution under Unified Hybrid Censoring

2021 ◽  
Vol 50 (1) ◽  
pp. 59-73
Author(s):  
Young Eun Jeon ◽  
Suk-Bok Kang
Keyword(s):  
Posterior Distribution ◽  
Mean Squared Error ◽  
Scale Parameter ◽  
Interval Estimation ◽  
Credible Interval ◽  
Rayleigh Distribution ◽  
Bayes Estimator ◽  
Hybrid Censoring ◽  
The Mean ◽  
Censoring Scheme

We derive some estimators of the scale parameter of the Rayleigh distribution under the unified hybrid censoring scheme. We also derive some estimators of the reliability function and the entropy of the Rayleigh distribution. First, we obtain the maximum likelihood estimator of the scale parameter. Second, we obtain the Bayes estimator using the mean of the posterior distribution. Lastly, we obtain the Bayes estimator using the mode of the posterior distribution. We also derive the interval estimation (confidence interval, credible interval, and HPD credible interval) for the scale parameter under the unified hybrid censoring scheme. We compare the proposed estimators in the sense of the mean squared error through Monte Carlo simulation. Coverage probability and average lengths of 95 % and 90% intervals are obtained.

scholarly journals On double stage minimax-shrinkage estimator for generalized Rayleigh model

2016 ◽  
Vol 5 (1) ◽  
pp. 39 ◽  
Author(s):  
Abbas Najim Salman ◽  
Maymona Ameen
Keyword(s):  
Sample Size ◽  
Shape Parameter ◽  
Mean Squared Error ◽  
Scale Parameter ◽  
Rayleigh Distribution ◽  
Shrinkage Estimator ◽  
Squared Error ◽  
Expected Sample Size ◽  
Generalized Rayleigh Distribution ◽  
The Mean

<p>This paper is concerned with minimax shrinkage estimator using double stage shrinkage technique for lowering the mean squared error, intended for estimate the shape parameter (a) of Generalized Rayleigh distribution in a region (R) around available prior knowledge (a<sub>0</sub>) about the actual value (a) as initial estimate in case when the scale parameter (l) is known .</p><p>In situation where the experimentations are time consuming or very costly, a double stage procedure can be used to reduce the expected sample size needed to obtain the estimator.</p><p>The proposed estimator is shown to have smaller mean squared error for certain choice of the shrinkage weight factor y(<strong>×</strong>) and suitable region R.</p><p>Expressions for Bias, Mean squared error (MSE), Expected sample size [E (n/a, R)], Expected sample size proportion [E(n/a,R)/n], probability for avoiding the second sample and percentage of overall sample saved  for the proposed estimator are derived.</p><p>Numerical results and conclusions for the expressions mentioned above were displayed when the consider estimator are testimator of level of significanceD.</p><p>Comparisons with the minimax estimator and with the most recent studies were made to shown the effectiveness of the proposed estimator.</p>

scholarly journals Two Different Classes of Shrinkage Estimators for the Scale Parameter of the Rayleigh Distribution

2021 ◽  
Vol 19 (1) ◽  
pp. 2-21
Author(s):  
Talha Omer ◽  
Zawar Hussain ◽  
Muhammad Qasim ◽  
Said Farooq Shah ◽  
Akbar Ali Khan
Keyword(s):  
Simulation Study ◽  
Mean Squared Error ◽  
Scale Parameter ◽  
Rayleigh Distribution ◽  
Shrinkage Estimators ◽  
Unbiased Estimators ◽  
Squared Error ◽  
The Mean ◽  
Simulation Results

Shrinkage estimators are introduced for the scale parameter of the Rayleigh distribution by using two different shrinkage techniques. The mean squared error properties of the proposed estimator have been derived. The comparison of proposed classes of the estimators is made with the respective conventional unbiased estimators by means of mean squared error in the simulation study. Simulation results show that the proposed shrinkage estimators yield smaller mean squared error than the existence of unbiased estimators.

Estimation of Stress–Strength Reliability from Exponentiated Inverse Rayleigh Distribution

2019 ◽  
Vol 26 (01) ◽  
pp. 1950005 ◽  
Author(s):  
G. Srinivasa Rao ◽  
Sauda Mbwambo ◽  
P. K. Josephat
Keyword(s):  
Carbon Fibers ◽  
Mean Squared Error ◽  
Scale Parameter ◽  
Average Length ◽  
Rayleigh Distribution ◽  
Squared Error ◽  
Coverage Probabilities ◽  
Common Scale ◽  
Asymptotic Confidence Intervals ◽  
The Mean

This paper considers the estimation of stress–strength reliability when two independent exponential inverse Rayleigh distributions with different shape parameters and common scale parameter. The maximum likelihood estimator (MLE) of the reliability, its asymptotic distribution and asymptotic confidence intervals are constructed. Comparisons of the performance of the estimators are carried out using Monte Carlo simulations, the mean squared error (MSE), bias, average length and coverage probabilities. Finally, a demonstration is delivered on how the proposed reliability model may be applied in data analysis of the strength data for single carbon fibers test data.

scholarly journals Exact Likelihood Inference for an Exponential Parameter under Generalized Adaptive Progressive Hybrid Censoring

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1149 ◽  
Author(s):  
Hyojin Lee ◽  
Kyeongjun Lee
Keyword(s):  
Scale Parameter ◽  
Moment Generating Function ◽  
Likelihood Inference ◽  
Exponential Parameter ◽  
Hybrid Censoring ◽  
Lower Confidence ◽  
Lower Confidence Bound ◽  
New Type ◽  
The Moment ◽  
Censoring Scheme

In this paper, we propose a new type censoring scheme named a generalized adaptive progressive hybrid censoring scheme (GenAdPrHyCS). In this new type censoring scheme, the experiment is assured to stop at a pre-assigned time. This censoring scheme is designed to correct the drawbacks in the AdPrHyCS. Furthermore, we discuss inference for one parameter exponential distribution (ExD) under GenAdPrHyCS. We derive the moment generating function of the maximum likelihood estimator (MLE) of scale parameter of ExD and the resulting lower confidence bound under GenAdPrHyCS.

scholarly journals Applying the Shrinkage Technique for Estimating the Scale Parameter of Weighted Rayleigh Distribution

2020 ◽  
pp. 2335-2340
Author(s):  
Intesar Obeid Hassoun ◽  
Adel Abdulkadhim Hussein
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Mean Squared Error ◽  
Scale Parameter ◽  
Rayleigh Distribution ◽  
Squared Error ◽  
Simulation Based

This paper includes the estimation of the scale parameter of weighted Rayleigh distribution using well-known methods of estimation (classical and Bayesian). The proposed estimators were compared using Monte Carlo simulation based on mean squared error (MSE) criteria. Then, all the results of simulation and comparisons were demonstrated in tables. 

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 On empirical Bayes estimation of multivariate regression coefficient

2006 ◽  
Vol 2006 ◽  
pp. 1-18
Author(s):  
R. J. Karunamuni ◽  
L. Wei
Keyword(s):  
Multivariate Regression ◽  
Empirical Bayes ◽  
Mean Squared Error ◽  
Bayes Estimator ◽  
Bayes Estimation ◽  
Empirical Bayes Estimation ◽  
Squared Error Loss ◽  
Squared Error ◽  
The Mean ◽  
Empirical Bayes Estimator

We investigate the empirical Bayes estimation problem of multivariate regression coefficients under squared error loss function. In particular, we consider the regression modelY=Xβ+ε, whereYis anm-vector of observations,Xis a knownm×kmatrix,βis an unknownk-vector, andεis anm-vector of unobservable random variables. The problem is squared error loss estimation ofβbased on some “previous” dataY1,…,Ynas well as the “current” data vectorYwhenβis distributed according to some unknown distributionG, whereYisatisfiesYi=Xβi+εi,i=1,…,n. We construct a new empirical Bayes estimator ofβwhenεi∼N(0,σ2Im),i=1,…,n. The performance of the proposed empirical Bayes estimator is measured using the mean squared error. The rates of convergence of the mean squared error are obtained.

scholarly journals Bayesian Generalized Self Method to Estimate Scale Parameter of Invers Rayleigh Distribution

CAUCHY ◽  
2021 ◽  
Vol 6 (4) ◽  
pp. 270-278
Author(s):  
Ferra Yanuar ◽  
Rahmi Febriyuni ◽  
Izzati Rahmi HG
Keyword(s):  
Exponential Distribution ◽  
Loss Function ◽  
Posterior Distribution ◽  
Scale Parameter ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Selection Model ◽  
The Real ◽  
Error Loss ◽  
Jeffrey's Prior

The purposes of this study are to estimate the scale parameter of Invers Rayleigh distribution under MLE and Bayesian Generalized square error loss function (SELF). The posterior distribution is considered to use two types of prior, namely Jeffrey’s prior and exponential distribution. The proposed methods are then employed in the real data. Several criteria for the selection model are considered in order to identify the method which results in a suitable value of parameter estimated. This study found that Bayesian Generalized SELF under Jeffrey’s prior yielded better estimation values that MLE and Bayesian Generalized SELF under exponential distribution.

scholarly journals Multicomponent Inverse Lomax Stress-Strength Reliability

2020 ◽  
pp. 72-80
Author(s):  
Nada S. Karam ◽  
Shahbaa M. Yousif ◽  
Bushra J. Tawfeeq
Keyword(s):  
Maximum Likelihood ◽  
Mean Squared Error ◽  
Scale Parameter ◽  
Model Systems ◽  
Estimation Methods ◽  
Squared Error ◽  
Mathematical Expressions ◽  
Distribution Parameters ◽  
The Mean ◽  
Inverse Lomax Distribution

In this article we derive two reliability mathematical expressions of two kinds of s-out of -k stress-strength model systems; and . Both stress and strength are assumed to have an Inverse Lomax distribution with unknown shape parameters and a common known scale parameter. The increase and decrease in the real values of the two reliabilities are studied according to the increase and decrease in the distribution parameters. Two estimation methods are used to estimate the distribution parameters and the reliabilities, which are Maximum Likelihood and Regression. A comparison is made between the estimators based on a simulation study by the mean squared error criteria, which revealed that the maximum likelihood estimator works the best.

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