A family of bayes estimators for doubly censored Weibull distribution

2020 ◽  
Vol 23 (4) ◽  
pp. 737-759
Author(s):  
Navid Feroze ◽  
Muhammad Aslam
Keyword(s):  
Weibull Distribution ◽  
Bayes Estimators ◽  
Doubly Censored

scholarly journals On the Estimation of Reliability of Weighted Weibull Distribution: A Comparative Study

2016 ◽  
Vol 5 (4) ◽  
pp. 1
Author(s):  
Bander Al-Zahrani
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Real Data ◽  
Reliability Function ◽  
Nonparametric Methods ◽  
Empirical Method ◽  
Density Estimator ◽  
Bayes Estimators ◽  
Unknown Parameters ◽  
Data Set

The paper gives a description of estimation for the reliability function of weighted Weibull distribution. The maximum likelihood estimators for the unknown parameters are obtained. Nonparametric methods such as empirical method, kernel density estimator and a modified shrinkage estimator are provided. The Markov chain Monte Carlo method is used to compute the Bayes estimators assuming gamma and Jeffrey priors. The performance of the maximum likelihood, nonparametric methods and Bayesian estimators is assessed through a real data set.

scholarly journals Bayesian Estimation of the Scale Parameter of Inverse Weibull Distribution under the Asymmetric Loss Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Farhad Yahgmaei ◽  
Manoochehr Babanezhad ◽  
Omid S. Moghadam
Keyword(s):  
Weibull Distribution ◽  
Scale Parameter ◽  
Loss Functions ◽  
Simulation Studies ◽  
Bayes Estimators ◽  
Likelihood Estimator ◽  
Risk Functions ◽  
Inverse Weibull Distribution ◽  
The Mean ◽  
Mean Square Errors

This paper proposes different methods of estimating the scale parameter in the inverse Weibull distribution (IWD). Specifically, the maximum likelihood estimator of the scale parameter in IWD is introduced. We then derived the Bayes estimators for the scale parameter in IWD by considering quasi, gamma, and uniform priors distributions under the square error, entropy, and precautionary loss functions. Finally, the different proposed estimators have been compared by the extensive simulation studies in corresponding the mean square errors and the evolution of risk functions.

scholarly journals Bayesian Modeling of 3-Component Mixture of Exponentiated Inverted Weibull Distribution under Noninformative Prior

2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Ammara Nawaz Cheema ◽  
Muhammad Aslam ◽  
Ibrahim M. Almanjahie ◽  
Ishfaq Ahmad
Keyword(s):  
Weibull Distribution ◽  
Research Work ◽  
Real Data ◽  
Loss Functions ◽  
Type I ◽  
Bayes Estimators ◽  
Component Mixture ◽  
Type I Censoring ◽  
Censoring Technique ◽  
The Impact

Bayesian study of 3-component mixture modeling of exponentiated inverted Weibull distribution under right type I censoring technique is conducted in this research work. The posterior distribution of the parameters is obtained assuming the noninformative (Jeffreys and uniform) priors. The different loss functions (squared error, quadratic, precautionary, and DeGroot loss function) are used to obtain the Bayes estimators and posterior risks. The performance of the Bayes estimators through posterior risks under the said loss functions is investigated through simulation process. Real data analysis of tensile strength of carbon fiber is also applied for 3 components to conclude the presentation of Bayes estimators. The limiting expressions are also elaborated for Bayes estimators and posterior risks in this study. The impact of some test termination times and sample sizes is reported on Bayes estimators.

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 Bayes Estimation of Shape Parameter of Length Biased Weibull Distribution

2021 ◽  
Vol 5 (1) ◽  
pp. 28
Author(s):  
Arun Kumar Rao ◽  
Himanshu Pandey
Keyword(s):  
Weibull Distribution ◽  
Bayesian Analysis ◽  
Shape Parameter ◽  
Bayes Estimation ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Squared Error

In this paper, length biased Weibull distribution is considered for Bayesian analysis. The expressions for Bayes estimators of the parameter have been derived under squared error, precautionary, entropy, K-loss, and Al-Bayyati’s loss functions by using quasi and gamma priors.

scholarly journals Bayesian Estimation for Two Parameters of Weibull Distribution under Generalized Weighted Loss Function

2021 ◽  
Vol 34 (4) ◽  
pp. 116-129
Author(s):  
Abtisam J. Kadhim ◽  
Huda A. Rasheed
Keyword(s):  
Weibull Distribution ◽  
Bayesian Estimation ◽  
Loss Function ◽  
Simulation Method ◽  
Bayes Estimators ◽  
Mean Squared Errors ◽  
Scale Parameters ◽  
The Mean ◽  
Two Parameters

In this paper, Bayes estimators for the shape and scale parameters of Weibull distribution have been obtained using the generalized weighted loss function, based on Exponential priors. Lindley’s approximation has been used effectively in Bayesian estimation. Based on theMonte Carlo simulation method, those estimators are compared depending on the mean squared errors (MSE’s).

scholarly journals Estimation of the Parameters for the Exponentiated Weibull Distribution Based on Progressive Type-II Censoring Scheme

2020 ◽  
Vol 9 (5) ◽  
pp. 1
Author(s):  
Mohammed Mohammed Ahmed Almazah
Keyword(s):  
Weibull Distribution ◽  
Loss Functions ◽  
Type Ii ◽  
Bayes Estimators ◽  
Shape Parameters ◽  
Censored Samples ◽  
Linex Loss ◽  
Progressive Type ◽  
Exponentiated Weibull Distribution ◽  
Exponentiated Weibull

The main objective of the present study is to find the estimation of the two Exponentiated Weibull distribution parameters, based on progressive Type II censored samples. The maximum likelihood and Bayes estimators for the two shape parameters and the scale parameter of the exponentiated Weibull lifetime model were derived. Bayes estimators was obtained by using both the symmetric and asymmetric loss functions via squared error loss and linex loss functions This was done with respect to the conjugate priors for two shape parameters. We used an approximation based on the Lindley (Trabajos de Estadistca) method for obtaining Bayes estimates under these loss functions. The different proposed estimators have been compared through an extensive simulation studies. Bayes ratings also turned out to be better than MLE. Whatever the sample sizes are, we get the same results.

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