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 Bayesian Inference of Burr Type VIII Distribution Based on Censored Samples

2014 ◽  
Vol 2014 ◽  
pp. 1-21
Author(s):  
Navid Feroz
Keyword(s):  
Bayesian Inference ◽  
Loss Function ◽  
Simulation Study ◽  
Bayes Estimation ◽  
Loss Functions ◽  
Quadratic Loss ◽  
Bayes Estimators ◽  
Type Viii ◽  
Censored Samples ◽  
Made In

This paper is concerned with estimation of the parameter of Burr type VIII distribution under a Bayesian framework using censored samples. The Bayes estimators and associated risks have been derived under the assumption of five priors and three loss functions. The comparison among the performance of different estimators has been made in terms of posterior risks. A simulation study has been conducted in order to assess and compare the performance of different estimators. The study proposes the use of inverse Levy prior based on quadratic loss function for Bayes estimation of the said parameter.

scholarly journals Bayes Estimators of Exponentiated Inverse Rayleigh Distribution using Lindleys Approximation

2021 ◽  
pp. 60-71
Author(s):  
Bashiru Omeiza Sule ◽  
Taiwo Mobolaji Adegoke ◽  
Kafayat Tolani Uthman
Keyword(s):  
Loss Function ◽  
Posterior Distribution ◽  
Real Life ◽  
Rayleigh Distribution ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Shape Parameters ◽  
True Parameter ◽  
Squared Error Loss Function ◽  
Scale Parameters

In this paper, Bayes estimators of the unknown shape and scale parameters of the Exponentiated Inverse Rayleigh Distribution (EIRD) have been derived using both the frequentist and bayesian methods. The Bayes theorem was adopted to obtain the posterior distribution of the shape and scale parameters of an Exponentiated Inverse Rayleigh Distribution (EIRD) using both conjugate and non-conjugate prior distribution under different loss functions (such as Entropy Loss Function, Linex Loss Function and Scale Invariant Squared Error Loss Function). The posterior distribution derived for both shape and scale parameters are intractable and a Lindley approximation was adopted to obtain the parameters of interest. The loss function were employed to obtain the estimates for both scale and shape parameters with an assumption that the both scale and shape parameters are unknown and independent. Also the Bayes estimate for the simulated datasets and real life datasets were obtained. The Bayes estimates obtained under dierent loss functions are close to the true parameter value of the shape and scale parameters. The estimators are then compared in terms of their Mean Square Error (MSE) using R programming language. We deduce that the MSE reduces as the sample size (n) increases.

scholarly journals The Bayesian Estimation for The Shape Parameter of The Power Function Distribution (PFD-I) to Use Hyper Prior Functions

2021 ◽  
Vol 27 (127) ◽  
pp. 229-252
Author(s):  
Jinan Abbas Naser Al-obedy
Keyword(s):  
Maximum Likelihood ◽  
Exponential Distribution ◽  
Power Function ◽  
Loss Function ◽  
Shape Parameter ◽  
Loss Functions ◽  
Erlang Distribution ◽  
Bayes Estimators ◽  
Function Distribution ◽  
Power Function Distribution

The objective of this study is to examine the properties of Bayes estimators of the shape parameter of the Power Function Distribution (PFD-I), by using two different prior distributions for the parameter θ and different loss functions that were compared with the maximum likelihood estimators. In many practical applications, we may have two different prior information about the prior distribution for the shape parameter of the Power Function Distribution, which influences the parameter estimation. So, we used two different kinds of conjugate priors of shape parameter θ of the Power Function Distribution (PFD-I) to estimate it. The conjugate prior function of the shape parameter θ was considered as a combination of two different prior distributions such as gamma distribution with Erlang distribution and Erlang distribution with exponential distribution and Erlang distribution with non-informative distribution and exponential distribution with the non-informative distribution. We derived Bayes estimators for shape parameter θ of the Power Function Distribution (PFD-I) according to different loss functions such as the squared error loss function (SELF), the weighted error loss function (WSELF) and modified linear exponential (MLINEX) loss function (MLF), with two different double priors. In addition to the classical estimation (maximum likelihood estimation). We used simulation to get the results of this study, for different cases of the shape parameter of the Power Function Distribution used to generate data for different samples sizes.

scholarly journals Bayesian Analysis of Weibull-Lindley Distribution Using Different Loss Functions

2020 ◽  
pp. 28-41
Author(s):  
Innocent Boyle Eraikhuemen ◽  
Olateju Alao Bamigbala ◽  
Umar Alhaji Magaji ◽  
Bassa Shiwaye Yakura ◽  
Kabiru Ahmed Manju
Keyword(s):  
Bayesian Analysis ◽  
Loss Function ◽  
Bayesian Methods ◽  
Shape Parameter ◽  
Loss Functions ◽  
Quadratic Loss ◽  
Function Estimation ◽  
Lindley Distribution ◽  
Method Of Maximum Likelihood ◽  
Parameter Values

In the present paper, a three-parameter Weibull-Lindley distribution is considered for Bayesian analysis. The estimation of a shape parameter of Weibull-Lindley distribution is obtained with the help of both the classical and Bayesian methods. Bayesian estimators are obtained by using Jeffrey’s prior, uniform prior and Gamma prior under square error loss function, quadratic loss function and Precautionary loss function. Estimation by the method of Maximum likelihood is also discussed. These methods are compared by using mean square error through simulation study with varying parameter values and sample sizes.

scholarly journals A Comparison between Maximum Likelihood and Bayesian Estimation Methods for a Shape Parameter of the Weibull-Exponential Distribution

2018 ◽  
pp. 1-12
Author(s):  
Terna G. Ieren ◽  
Pelumi E. Oguntunde
Keyword(s):  
Maximum Likelihood ◽  
Exponential Distribution ◽  
Loss Function ◽  
Shape Parameter ◽  
Estimation Methods ◽  
Quadratic Loss ◽  
Posterior Distributions ◽  
Bayes Estimators ◽  
Method Of Maximum Likelihood ◽  
Parameter Values

We considered the Bayesian analysis of a shape parameter of the Weibull-Exponential distribution in this paper. We assumed a class of non-informative priors in deriving the corresponding posterior distributions. In particular, the Bayes estimators and associated risks were calculated under three different loss functions. The performance of the Bayes estimators was evaluated and compared to the method of maximum likelihood under a comprehensive simulation study. It was discovered that for the said parameters to be estimated, the quadratic loss function under both uniform and Jeffrey’s priors should be used for decreasing parameter values while the use of precautionary loss function can be preferred for increasing parameter values irrespective of the variations in sample size.  

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 Bayesian Approach in Estimation of Shape Parameter of an Exponential Inverse Exponential Distribution

2020 ◽  
pp. 13-27
Author(s):  
Bashiru Omeiza Sule ◽  
Taiwo Mobolaji Adegoke
Keyword(s):  
Exponential Distribution ◽  
Gamma Distribution ◽  
Loss Function ◽  
Posterior Distribution ◽  
Prior Distribution ◽  
Shape Parameter ◽  
Real Life ◽  
Loss Functions ◽  
Jeffreys Prior ◽  
True Parameter

Aims: This study aimed to obtain the shape parameter of an Exponential Inverted Exponential distribution using different prior distributions under different loss functions. Methodology: The Bayes’ theorem was adopted to obtain the posterior distribution of the shape parameter of an Exponential inverted Exponential distribution for both non-information prior (such as Jeffreys prior, Hartigen prior and Uniform prior) and an informative prior (such as Gamma distribution and chi-square distribution). Different loss functions (such as Entropy loss function, Square error loss function, Al-Bayyati’s loss function and Precautionary loss function) were employed to obtain the estimate parameter of the shape parameter with an assumption that the scale parameter is known. Results: The posterior distribution of the shape parameter of an Exponential Inverted Exponential distribution follows a Gamma distribution for all the prior distribution in the study. Also the Bayes estimate for the simulated datasets and real life dataset were obtained. Conclusion: The Bayes’ estimates for different prior distribution under different loss functions are close to the true parameter value of the shape parameter. The estimators are then compared in terms of their Mean Square Error (MSE) which is computed using R programming language. We deduce that the MSE reduces as the sample size (n) increases.

scholarly journals Bayes Estimation under Conjugate Prior for the Case of Laplace Double Exponential Distribution

2018 ◽  
Vol 40 (1) ◽  
pp. 151-168
Author(s):  
Md Habibur Rahman ◽  
MK Roy
Keyword(s):  
Bayesian Estimation ◽  
Exponential Distribution ◽  
Loss Function ◽  
Real Life ◽  
Bayes Estimation ◽  
Loss Functions ◽  
Quadratic Loss ◽  
Squared Error Loss Function ◽  
Double Exponential Distribution ◽  
Double Exponential

The Bayesian estimation approach is a non-classical device in the estimation part of statistical inference which is very useful in real world situation. The main objective of this paper is to study the Bayes estimators of the parameter of Laplace double exponential distribution. In Bayesian estimation loss function, prior distribution and posterior distribution are the most important ingredients. In real life we try to minimize the loss and want to know some prior information about the problem to solve it accurately. The well known conjugate priors are considered for finding the Bayes estimator. In our study we have 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. The performance of the obtained estimators for different types of loss functions are then compared among themselves as well as with the classical maximum likelihood estimator (MLE). Mean Square Error (MSE) of the estimators are also computed and presented in graphs. The Chittagong Univ. J. Sci. 40 : 151-168, 2018

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