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 Comparison of Bayes Estimators for Parameter and Relia-bility Function for Inverse Rayleigh Distribution by Using Generalized Square Error Loss Function

2018 ◽  
Vol 28 (2) ◽  
pp. 162
Author(s):  
Huda A. Rasheed
Keyword(s):  
Loss Function ◽  
Scale Parameter ◽  
Reliability Function ◽  
Rayleigh Distribution ◽  
Squared Error Loss Function ◽  
Squared Error Loss ◽  
Mean Squared Errors ◽  
Error Loss ◽  
Squared Error ◽  
Informative Prior

In the current study, we have been derived some Basyian estimators for the parameter and relia-bility function of the inverse Rayleigh distribution under Generalized squared error loss function. In order to get the best understanding of the behavior of Bayesian analysis, we consider non-informative prior for the scale parameter using Jefferys prior Information as well as informative prior density represented by Gamma distribution. Monte-Carlo simulation have been employed to compare the behavior of different estimates for the scale parameter and reliability function of in-verse Rayleigh distribution based on mean squared errors and Integrated mean squared errors, respectively. In the current study, we observed that more occurrence of Bayesian estimate using Generalized squared error loss function using Gamma prior is better than other estimates for all cases

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>

Bayesian Reliability Estmation with a Truncated Normal Prior

1988 ◽  
Vol 37 (3-4) ◽  
pp. 227-231 ◽  
Author(s):  
Samir K. Bhattacharya ◽  
Ravindar K. Tyagi
Keyword(s):  
Bayesian Estimation ◽  
Parameter Space ◽  
Loss Function ◽  
Exponential Model ◽  
Life Testing ◽  
Squared Error Loss Function ◽  
Squared Error Loss ◽  
Squared Error ◽  
Life Tests ◽  
Truncated Normal

Beyesian reliebility estimation for the exponential model. based on life tests that are terminated after a preassigned number of failures, is carried out under the assumption of the squared error loss function and a truncated normal priod density on the parameter space. The Bayesian estimation of reliability for the case of ‘attribute life testing’ is also discussed.

scholarly journals Bayesian Estimation and Prediction of Discrete Gompertz Distribution

2021 ◽  
pp. 1-21
Author(s):  
M. A. Hegazy ◽  
R. E. Abd El-Kader ◽  
A. A. El-Helbawy ◽  
G. R. Al-Dayian
Keyword(s):  
Bayesian Estimation ◽  
Loss Function ◽  
Hazard Rate ◽  
Squared Error Loss Function ◽  
Squared Error Loss ◽  
Gompertz Distribution ◽  
Estimation And Prediction ◽  
Error Loss ◽  
Squared Error ◽  
Rate Functions

In this paper, Bayesian inference is used to estimate the parameters, survival, hazard and alternative hazard rate functions of discrete Gompertz distribution. The Bayes estimators are derived under squared error loss function as a symmetric loss function and linear exponential loss function as an asymmetric loss function. Credible intervals for the parameters, survival, hazard and alternative hazard rate functions are obtained. Bayesian prediction (point and interval) for future observations of discrete Gompertz distribution based on two-sample prediction are investigated. A numerical illustration is carried out to investigate the precision of the theoretical results of the Bayesian estimation and prediction on the basis of simulated and real data. Regarding the results of simulation seems to perform better when the sample size increases and the level of censoring decreases. Also, in most cases the results under the linear exponential loss function is better than the corresponding results under squared error loss function. Two real lifetime data sets are used to insure the simulated results.

scholarly journals Bayesian and Non - Bayesian Inference for Shape Parameter and Reliability Function of Basic Gompertz Distribution

2020 ◽  
Vol 17 (3) ◽  
pp. 0854
Author(s):  
Manahel Awad ◽  
Huda Rashed
Keyword(s):  
Shape Parameter ◽  
Simulation Method ◽  
Reliability Function ◽  
Monte Carlo Simulation Method ◽  
Scale Invariant ◽  
Squared Error Loss Function ◽  
Gompertz Distribution ◽  
Mean Squared Errors ◽  
Squared Error ◽  
Informative Prior

In this paper, some estimators of the unknown shape parameter and reliability function  of Basic Gompertz distribution (BGD) have been obtained, such as MLE, UMVUE, and MINMSE, in addition to estimating Bayesian estimators under Scale invariant squared error loss function assuming informative prior represented by Gamma distribution and non-informative prior by using Jefferys prior. Using Monte Carlo simulation method, these estimators of the shape parameter and R(t), have been compared based on mean squared errors and integrated mean squared, respectively

scholarly journals E-Bayesian Estimation of Chen Distribution Based on Type-I Censoring Scheme

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 636 ◽  
Author(s):  
Ali Algarni ◽  
Abdullah M. Almarashi ◽  
Hassan Okasha ◽  
Hon Keung Tony Ng
Keyword(s):  
Bayesian Estimation ◽  
Loss Function ◽  
Scale Parameter ◽  
Type I ◽  
Squared Error Loss Function ◽  
Squared Error Loss ◽  
Type I Censoring ◽  
Squared Error ◽  
Censoring Scheme ◽  
Bayesian Estimators

In this paper, E-Bayesian estimation of the scale parameter, reliability and hazard rate functions of Chen distribution are considered when a sample is obtained from a type-I censoring scheme. The E-Bayesian estimators are obtained based on the balanced squared error loss function and using the gamma distribution as a conjugate prior for the unknown scale parameter. Also, the E-Bayesian estimators are derived using three different distributions for the hyper-parameters. Some properties of E-Bayesian estimators based on balanced squared error loss function are discussed. A simulation study is performed to compare the efficiencies of different estimators in terms of minimum mean squared errors. Finally, a real data set is analyzed to illustrate the applicability of the proposed estimators.

scholarly journals A Comparison of Bayes Estimators for the parameter of Rayleigh Distribution with Simulation

2018 ◽  
Vol 24 (106) ◽  
pp. 49
Author(s):  
جنان عباس ناصر
Keyword(s):  
Loss Function ◽  
Prior Distribution ◽  
Mean Squared Error ◽  
Rayleigh Distribution ◽  
Square Root ◽  
Bayes Estimators ◽  
Squared Error Loss Function ◽  
Squared Error Loss ◽  
True Value ◽  
Squared Error

   A comparison of double informative and non- informative priors assumed for the parameter of Rayleigh distribution is considered. Three different sets of double priors are included, for a single unknown parameter of Rayleigh distribution. We have assumed three double priors: the square root inverted gamma (SRIG) - the natural conjugate family of priors distribution, the square root inverted gamma – the non-informative distribution, and the natural conjugate family of priors - the non-informative distribution as double priors .The data is generating form three cases from Rayleigh distribution for different samples sizes (small, medium, and large). And Bayes estimators for the parameter is derived under a squared error loss function and weighted squared error loss function) in the cases of the three different sets of prior distributions .Simulations is employed to obtain results. And determine the best estimator according to the smallest value of mean squared error and weighted mean squared error. We found  that the best estimation for the parameter for all sample sizes (n) , when the double prior distribution for  is SRIG - the natural conjugate family of priors distribution with values (a=5, b=0.5, =8, =0.5) and (a=8, b=1, =5, =1) for the  true value of  respectively .Also ,we obtained the best estimation for  when the double prior distribution for  is the natural conjugate family of priors-non-informative distribution with values(=0.5, =5, c=1) for  the true value of ().  

scholarly journals Bayesian Estimation under Different Loss Functions Using Gamma Prior for the Case of Exponential Distribution

2017 ◽  
Vol 9 (1) ◽  
pp. 67-78
Author(s):  
M. R. Hasan ◽  
A. R. Baizid
Keyword(s):  
Bayesian Estimation ◽  
Exponential Distribution ◽  
Loss Function ◽  
Mean Squared Error ◽  
Simulated Data ◽  
Life Time ◽  
Loss Functions ◽  
Quadratic Loss ◽  
Squared Error Loss Function ◽  
Squared Error

The Bayesian estimation approach is a non-classical estimation technique in statistical inference and is very useful in real world situation. The aim of this paper is to study the Bayes estimators of the parameter of exponential distribution under different loss functions and compared among them as well as with the classical estimator named maximum likelihood estimator (MLE). Since exponential distribution is the life time distribution, we have studied exponential distribution using gamma prior. Here the gamma prior is used as the prior distribution of exponential distribution for finding the Bayes estimator. In our study we also used different symmetric and asymmetric loss functions such as squared error loss function, quadratic loss function, modified linear exponential (MLINEX) loss function and non-linear exponential (NLINEX) loss function. We have used simulated data using R-coding to find out the mean squared error (MSE) of different loss functions and hence found that non-classical estimator is better than classical estimator. Finally, mean square error (MSE) of the estimators of different loss functions are presented graphically.

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