scholarly journals Bayes approach to study shape parameter of Frechet distribution

2015 ◽  
Vol 4 (3) ◽  
pp. 246 ◽  
Author(s):  
Wajiha Nasir ◽  
Muhammad Aslam
Keyword(s):  
Shape Parameter ◽  
Loss Functions ◽  
Type Ii ◽  
Posterior Distributions ◽  
Bayes Estimators ◽  
Integration Technique ◽  
Monte Carlo Simulation Study ◽  
Fréchet Distribution ◽  
Bayesian Paradigm ◽  
Frechet Distribution

<div><p>In this paper, Frechet distribution under Bayesian paradigm is studied. Posterior distributions are derived by using Gumbel Type-II and Levy prior. Quadrature numerical integration technique is utilized to solve posterior distribution. Bayes estimators and their risks have been obtained by using four loss functions. Prior predictive distributions are derived for elicitation of hyperparameters. The performance of Bayes estimators are compared by using Monte Carlo simulation study.</p></div>

scholarly journals Bayesian Analysis of a Shape Parameter of the Weibull-Frechet Distribution

2018 ◽  
pp. 1-19
Author(s):  
Terna Godfrey Ieren ◽  
Angela Unna Chukwu
Keyword(s):  
Loss Function ◽  
Shape Parameter ◽  
Real Life ◽  
Loss Functions ◽  
Quadratic Loss ◽  
Bayes Estimators ◽  
Informative Priors ◽  
Fréchet Distribution ◽  
Minimum Bayes Risk ◽  
Frechet Distribution

In this paper, we estimate a shape parameter of the Weibull-Frechet distribution by considering the Bayesian approach under two non-informative priors using three different loss functions. We derive the corresponding posterior distributions for the shape parameter of the Weibull-Frechet distribution assuming that the other three parameters are known. The Bayes estimators and associated posterior               risks have also been derived using the three different loss functions. The performance of the Bayes estimators are evaluated and compared using a comprehensive simulation study and a real life application to find out the combination of a loss function and a prior having the minimum Bayes risk and hence producing the best results. In conclusion, this study reveals that in order to estimate the parameter in question, we should use quadratic loss function under either of the two non-informative priors used in this study.  

scholarly journals On estimation of Frechet distribution with known shape using Bayesian analysis under informative priors

2017 ◽  
Vol 5 (2) ◽  
pp. 141
Author(s):  
Wajiha Nasir
Keyword(s):  
Bayesian Analysis ◽  
Loss Function ◽  
Simulation Study ◽  
Posterior Distribution ◽  
Loss Functions ◽  
Quadratic Loss ◽  
Bayes Estimators ◽  
Informative Priors ◽  
Fréchet Distribution ◽  
Frechet Distribution

In this study, Frechet distribution has been studied by using Bayesian analysis. Posterior distribution has been derived by using gamma and exponential. Bayes estimators and their posterior risks has been derived using five different loss functions. Elicitation of hyperparameters has been done by using prior predictive distributions. Simulation study is carried out to study the behavior of posterior distribution. Quasi quadratic loss function and exponential prior are found better among all.

scholarly journals Parameter Estimation of Length Biased Weighted Frechet Distribution via Bayesian Approach

2021 ◽  
pp. 42-51
Author(s):  
Arun Kumar Rao ◽  
Himanshu Pandey
Keyword(s):  
Parameter Estimation ◽  
Bayesian Analysis ◽  
Bayesian Approach ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Fréchet Distribution ◽  
Squared Error ◽  
Frechet Distribution

In this paper, length-biased weighted Frechet 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 The Mixture of the Marshall–Olkin Extended Weibull Distribution under Type-II Censoring and Different Loss Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Refah Alotaibi ◽  
Mervat Khalifa ◽  
Lamya A. Baharith ◽  
Sanku Dey ◽  
H. Rezk
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Loss Functions ◽  
Residual Lifetime ◽  
Mean Deviation ◽  
Average Lifetime ◽  
Type Ii ◽  
Bayes Estimators ◽  
Monte Carlo Simulation Study ◽  
Extended Weibull Distribution

To study the heterogeneous nature of lifetimes of certain mechanical or engineering processes, a mixture model of some suitable lifetime distributions may be more appropriate and appealing as compared to simple models. This paper considers a mixture of the Marshall–Olkin extended Weibull distribution for efficient modeling of failure, survival, and COVID-19 data under classical and Bayesian perspectives based on type-II censored data. We derive several properties of the new distribution such as moments, incomplete moments, mean deviation, average lifetime, mean residual lifetime, Rényi entropy, Shannon entropy, and order statistics of the proposed distribution. Maximum likelihood and Bayes procedure are used to derive both point and interval estimates of the parameters involved in the model. Bayes estimators of the unknown parameters of the model are obtained under symmetric (squared error) and asymmetric (linear exponential (LINEX)) loss functions using gamma priors for both the shape and the scale parameters. Furthermore, approximate confidence intervals and Bayes credible intervals (CIs) are also obtained. Monte Carlo simulation study is carried out to assess the performance of the maximum likelihood estimators and Bayes estimators with respect to their estimated risk. The flexibility and importance of the proposed distribution are illustrated by means of four real datasets.

scholarly journals Bayes Estimation of a Two-Parameter Geometric Distribution under Multiply Type II Censoring

2011 ◽  
Vol 2011 ◽  
pp. 1-10
Author(s):  
J. B. Shah ◽  
M. N. Patel
Keyword(s):  
Geometric Distribution ◽  
Correct Choice ◽  
Bayes Estimation ◽  
Loss Functions ◽  
Type Ii ◽  
Expected Loss ◽  
Bayes Estimators ◽  
Linex Loss ◽  
Type Ii Censored Data ◽  
Two Parameter

We derive Bayes estimators of reliability and the parameters of a two- parameter geometric distribution under the general entropy loss, minimum expected loss and linex loss, functions for a noninformative as well as beta prior from multiply Type II censored data. We have studied the robustness of the estimators using simulation and we observed that the Bayes estimators of reliability and the parameters of a two-parameter geometric distribution under all the above loss functions appear to be robust with respect to the correct choice of the hyperparameters a(b) and a wrong choice of the prior parameters b(a) of the beta prior.

scholarly journals On Bayesian Analysis of Burr Type VII Distribution under Different Censoring Schemes

2012 ◽  
Vol 2012 ◽  
pp. 1-5
Author(s):  
Navid Feroze ◽  
Muhammad Aslam
Keyword(s):  
Comparative Study ◽  
Bayesian Analysis ◽  
Simulation Study ◽  
Type Ii ◽  
Posterior Distributions ◽  
Bayes Estimators ◽  
Type Ii Censoring ◽  
The Comparative Study ◽  
Posterior Estimation

This paper includes the Bayesian analysis of Burr type VII distribution. Three censoring schemes, namely, left censoring, singly type II censoring, and doubly type II censoring have been used for posterior estimation. The results of different censoring schemes have been compared with those under complete samples. The comparative study among the performance of different censoring schemes has also been made. Two noninformative (uniform and Jeffreys) priors have been assumed to derive the posterior distributions under each case. The performance of Bayes estimators has been compared in terms of posterior risks under a simulation study.

scholarly journals On Parameters Estimation of Lomax Distribution under General Progressive Censoring

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Bander Al-Zahrani ◽  
Mashail Al-Sobhi
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Parameters Estimation ◽  
Loss Functions ◽  
Mcmc Methods ◽  
Bayes Estimators ◽  
Progressive Censoring ◽  
Likelihood Estimator ◽  
Monte Carlo Simulation Study ◽  
Lomax Distribution

We consider the estimation problem of the probability S=P(Y<X) for Lomax distribution based on general progressive censored data. The maximum likelihood estimator and Bayes estimators are obtained using the symmetric and asymmetric balanced loss functions. The Markov chain Monte Carlo (MCMC) methods are used to accomplish some complex calculations. Comparisons are made between Bayesian and maximum likelihood estimators via Monte Carlo simulation study.

scholarly journals Bayes Estimation of the Reliability Function of Pareto Distribution Under Three Different Loss Functions

2020 ◽  
Author(s):  
Gaurav Shukla ◽  
Umesh Chandra ◽  
Vinod Kumar
Keyword(s):  
Shape Parameter ◽  
Pareto Distribution ◽  
Risk Function ◽  
Simulated Data ◽  
Reliability Function ◽  
Minimum Variance ◽  
Bayes Estimation ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Data Set

In this paper, we have proposed Bayes estimators of shape parameter of Pareto distribution as well as reliability function under SELF, QLF and APLF loss functions. For better understanding of Bayesian approach, we consider Jeffrey’s prior as non-informative prior, exponential and gamma priors as informative priors. The proposed estimators have been compared with Maximum likelihood estimator (MLE) and the uniformly minimum variance unbiased estimator (UMVUE). Moreover, the current study also derives the expressions for risk function under these three loss functions. The results obtained have been illustrated with the real as well as simulated data set.

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