scholarly journals Comparing Bayes Estimators With others , for scale parameter and Reliability function of two parameters Frechet distribution

2016 ◽  
Vol 22 (88) ◽  
pp. 1
Author(s):  
ميسون حميد فرج
Keyword(s):  
Scale Parameter ◽  
Reliability Function ◽  
Bayes Estimators ◽  
Fréchet Distribution ◽  
Two Parameters ◽  
Frechet Distribution

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 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 Optimization of mechanical properties of chitosan/phenol formaldehyde composite

2018 ◽  
Vol 11 (1) ◽  
pp. 229-235
Author(s):  
G.B. Iliasu ◽  
A.A. Kogo ◽  
M.K. Yakubu
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Loss Function ◽  
Scale Parameter ◽  
Seismic Analysis ◽  
Phenol Formaldehyde ◽  
Bayes Estimation ◽  
Fréchet Distribution ◽  
Frechet Distribution ◽  
Balance Loss

The Frechet distribution which has a scale and shape parameters, has been found to have wide application in modelling extreme events such as radioactive emission, flood, rainfall, seismic analysis, wind speed, etc. In this research paper, the Bayesian analysis of scale parameter of Frechet distribution was considered. It is necessary to know the best combination of prior distribution and loss function for the parameter estimation. Posterior distribution was derived by uniform and Jeffrey’s prior under the square error, Precautionary, Quadratic and Weighted balance loss function. Bayes estimation and their corresponding risk was obtained by the above stated priors and loss function. Monte Carlo simulations was conducted to compare the performance of the estimators. It is evident that weighted balance loss function when used with uniform prior provides the least posterior risk.Keywords: Frechet Distribution, Non-Informative Prior, Bayesian Estimation, Loss Functions, Monte Carlo Simulations

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.

Properties and methods of estimation for a bivariate exponentiated Fréchet distribution

2020 ◽  
Vol 70 (5) ◽  
pp. 1211-1230
Author(s):  
Abdus Saboor ◽  
Hassan S. Bakouch ◽  
Fernando A. Moala ◽  
Sheraz Hussain
Keyword(s):  
Maximum Likelihood ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Superior Performance ◽  
Estimation Methods ◽  
Conditional Probability Density ◽  
Data Set ◽  
Fréchet Distribution ◽  
Frechet Distribution

AbstractIn this paper, a bivariate extension of exponentiated Fréchet distribution is introduced, namely a bivariate exponentiated Fréchet (BvEF) distribution whose marginals are univariate exponentiated Fréchet distribution. Several properties of the proposed distribution are discussed, such as the joint survival function, joint probability density function, marginal probability density function, conditional probability density function, moments, marginal and bivariate moment generating functions. Moreover, the proposed distribution is obtained by the Marshall-Olkin survival copula. Estimation of the parameters is investigated by the maximum likelihood with the observed information matrix. In addition to the maximum likelihood estimation method, we consider the Bayesian inference and least square estimation and compare these three methodologies for the BvEF. A simulation study is carried out to compare the performance of the estimators by the presented estimation methods. The proposed bivariate distribution with other related bivariate distributions are fitted to a real-life paired data set. It is shown that, the BvEF distribution has a superior performance among the compared distributions using several tests of goodness–of–fit.

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.

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