scholarly journals Estimation of the scale parameter of gamma model in presence of outlier observations

1990 ◽  
Vol 13 (1) ◽  
pp. 121-127 ◽  
Author(s):  
M. E. Ghitany
Keyword(s):  
Shape Parameter ◽  
Scale Parameter ◽  
Point Estimation ◽  
Random Shape ◽  
Gamma Model ◽  
Squared Error Loss Function ◽  
Squared Error Loss ◽  
Testing Model ◽  
Squared Error ◽  
Two Parameter

This paper considers the Bayesian point estimation of the scale parameter for a two-parameter gamma life-testing model in presence of several outlier observations in the data. The Bayesian analysis is carried out under the assumption of squared error loss function and fixed or random shape parameter.

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 Bayesian Estimation of Parameters of Weibull Distribution Using Linex Error Loss Function

2020 ◽  
Vol 9 (2) ◽  
pp. 38
Author(s):  
Josphat. K. Kinyanjui ◽  
Betty. C. Korir
Keyword(s):  
Weibull Distribution ◽  
Loss Function ◽  
Scale Parameter ◽  
Risk Function ◽  
Bayes Estimators ◽  
Squared Error Loss Function ◽  
Squared Error Loss ◽  
Error Loss ◽  
Squared Error ◽  
Linex Loss

This paper develops a Bayesian analysis of the scale parameter in the Weibull distribution with a scale parameter  θ  and shape parameter  β (known). For the prior distribution of the parameter involved, inverted Gamma distribution has been examined. Bayes estimates of the scale parameter, θ  , relative to LINEX loss function are obtained. Comparisons in terms of risk functions of those under LINEX loss and squared error loss functions with their respective alternate estimators, viz: Uniformly Minimum Variance Unbiased Estimator (U.M.V.U.E) and Bayes estimators relative to squared error loss function are made. It is found that Bayes estimators relative to squared error loss function dominate the alternative estimators in terms of risk function.

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 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.

Lifetime Estimation for Web Game Based on Weibull Distribution

2014 ◽  
Vol 539 ◽  
pp. 456-459
Author(s):  
Hai Shu Yu ◽  
Yan Hua Yuan
Keyword(s):  
Weibull Distribution ◽  
Shape Parameter ◽  
Scale Parameter ◽  
Likelihood Estimation ◽  
Statistic Analysis ◽  
Lifetime Data ◽  
Lifetime Estimation ◽  
Proposed Model ◽  
Two Parameter ◽  
The Web

In order to make statistic analysis on lifetime data for web game, the two-parameter Weibull distribution was applied to describe its distribution. The shape parameter and the scale parameter were given by maximum likelihood estimation. When a web game followed Weibull distribution, the lifetime parameters are calculated via Matlab. The results show that the proposed model is appropriate to estimate the web game lifetime.

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.

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