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.

scholarly journals Pre-Test Single and Double Stage Shrunken Estimators for the Mean of Normal Distribution with Known Variance

2010 ◽  
Vol 7 (4) ◽  
pp. 1432-1441
Author(s):  
Baghdad Science Journal
Keyword(s):  
Sample Size ◽  
Normal Distribution ◽  
Relative Efficiency ◽  
Mean Squared Error ◽  
Numerical Results ◽  
Squared Error ◽  
Expected Sample Size ◽  
Test Region ◽  
Prior Estimate ◽  
The Mean

This paper is concerned with pre-test single and double stage shrunken estimators for the mean (?) of normal distribution when a prior estimate (?0) of the actule value (?) is available, using specifying shrinkage weight factors ?(?) as well as pre-test region (R). Expressions for the Bias [B(?)], mean squared error [MSE(?)], Efficiency [EFF(?)] and Expected sample size [E(n/?)] of proposed estimators are derived. Numerical results and conclusions are drawn about selection different constants included in these expressions. Comparisons between suggested estimators, with respect to classical estimators in the sense of Bias and Relative Efficiency, are given. Furthermore, comparisons with the earlier existing works are drawn.

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 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 A New Liu Type of Estimator for the Restricted SUR Estimator

2020 ◽  
Vol 18 (1) ◽  
pp. 2-11
Author(s):  
Kristofer Månsson ◽  
B. M. Golam Kibria ◽  
Ghazi Shukur
Keyword(s):  
Linear Subspace ◽  
Mean Squared Error ◽  
Shrinkage Estimator ◽  
Seemingly Unrelated Regression ◽  
Simulation Techniques ◽  
Squared Error ◽  
Unrelated Regression ◽  
The Mean

A new Liu type of estimator for the seemingly unrelated regression (SUR) models is proposed that may be used when estimating the parameters vector in the presence of multicollinearity if the it is suspected to belong to a linear subspace. The dispersion matrices and the mean squared error (MSE) are derived. The new estimator may have a lower MSE than the traditional estimators. It was shown using simulation techniques the new shrinkage estimator outperforms the commonly used estimators in the presence of multicollinearity.

scholarly journals Bayesian Estimation for the Centered Parameterization of the Skew-Normal Distribution

2017 ◽  
Vol 40 (1) ◽  
pp. 123-140 ◽  
Author(s):  
Paulino Pérez-Rodríguez ◽  
José A. Villaseñor ◽  
Sergio Pérez ◽  
Javier Suárez
Keyword(s):  
Normal Distribution ◽  
Shape Parameter ◽  
Mean Squared Error ◽  
Scale Parameter ◽  
Posterior Distributions ◽  
Skew Normal Distribution ◽  
Inference Problems ◽  
Squared Error ◽  
Practical Standpoint ◽  
Skew Normal

The skew-normal (SN) distribution is a generalization of the normal distribution, where a shape parameter is added to adopt skewed forms. The SN distribution has some of the properties of a univariate normal distribution, which makes it very attractive from a practical standpoint; however, it presents some inference problems. Specifically, the maximum likelihood estimator for the shape parameter tends to infinity with a positive probability. A new Bayesian approach is proposed in this paper which allows to draw inferences on the parameters of this distribution by using improper prior distributions in the ``centered parametrization'' for the location and scale parameter and a Beta-type for the shape parameter. Samples from posterior distributions are obtained by using the Metropolis-Hastings algorithm. A simulation study shows that the mode of the posterior distribution appears to be a good estimator in terms of bias and mean squared error. A comparative study with similar proposals for the SN estimation problem was undertaken. Simulation results provide evidence that the proposed method is easier to implement than previous ones. Some applications and comparisons are also included.

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.

Minimax Shrunken Technique for Estimate Burr X Distribution Shape Parameter

2018 ◽  
pp. 484
Author(s):  
Abbas Najim Salman ◽  
Maymona M. Ameen ◽  
A. E. Abdul-Nabi
Keyword(s):  
Relative Efficiency ◽  
Prior Information ◽  
Shape Parameter ◽  
Mean Squared Error ◽  
Scale Parameter ◽  
The Real ◽  
Squared Error ◽  
Distribution Shape ◽  
Original Estimate ◽  
Bias Ratio

      The present paper concern with minimax shrinkage estimator technique in order to estimate Burr X distribution shape parameter, when prior information about the real shape obtainable as original estimate while known scale parameter.  Derivation for Bias Ratio, Mean squared error and the Relative Efficiency equations.  Numerical results and conclusions for the expressions mentioned above were displayed. Comparisons for proposed estimator with most recent works were made.  

scholarly journals Bayesian estimation of the shape parameter of generalized Rayleigh distribution under non-informative prior

2015 ◽  
Vol 4 (1) ◽  
pp. 1
Author(s):  
Yakubu Aliyu ◽  
Abubakar Yahaya
Keyword(s):  
Bayesian Estimation ◽  
Loss Function ◽  
Shape Parameter ◽  
Rayleigh Distribution ◽  
Skewed Distribution ◽  
Time Data ◽  
Squared Error Loss Function ◽  
Squared Error ◽  
Informative Prior ◽  
Generalized Rayleigh Distribution

<p>A decade ago, two-parameter Burr Type X distribution was introduced by Surles and Padgett [14] which was described as Generalized Rayleigh Distribution (GRD). This skewed distribution can be used quiet effectively in modelling life time data. In this work, Bayesian estimation of the shape parameter of GRD was considered under the assumption of non-informative prior. The estimates were obtained under the squared error, Entropy and Precautionary loss functions. Extensive Monte Carlo simulations were carried out to compare the performances of the Bayes estimates with that of MLEs. It was observed that the estimate under the Entropy loss function is more stable than the estimates under squared error loss function, Precautionary loss function and MLEs.</p>

scholarly journals Preliminary test shrinkage estimators for the shape parameter of generalized exponential distribution

2016 ◽  
Vol 5 (4) ◽  
pp. 162
Author(s):  
Abbas Najim Salman ◽  
Rana Hadi
Keyword(s):  
Shape Parameter ◽  
Mean Squared Error ◽  
Scale Parameter ◽  
Preliminary Test ◽  
Shrinkage Estimators ◽  
Generalized Exponential Distribution ◽  
Initial Value ◽  
Squared Error ◽  
Optimal Region ◽  
Past Experiences

The present paper deals with the estimation of the shape parameter α of Generalized Exponential GE (α, λ) distribution when the scale parameter λ is known, by using preliminary test single stage shrinkage (SSS) estimator when a prior knowledge available about the shape parameter as initial value due past experiences as well as optimal region R for accepting this prior knowledge.The Expressions for the Bias [B (.)], Mean Squared Error [MSE] and Relative Efficiency [R.Eff (.)] for the proposed estimator is derived.Numerical results about conduct of the considered estimator are discussed include study the mentioned expressions. The numerical results exhibit and put it in tables.Comparisons between the proposed estimator  withe classical estimator  as well as with some earlier studies were made to show the effect and usefulness of the considered estimator.

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