scholarly journals A 3-component mixture of inverse Rayleigh distributions: properties and estimation in Bayesian framework

2016 ◽  
Vol 5 (2) ◽  
pp. 120
Author(s):  
Tabasam Sultana ◽  
Muhammad Aslam
Keyword(s):  
Survival Analysis ◽  
Prior Information ◽  
Bayesian Framework ◽  
Reliability Theory ◽  
Statistical Properties ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Informative Priors ◽  
Component Mixture ◽  
Censored Sampling

<p>This paper is about studying a 3-component mixture of the inverse Rayleigh distributions under Bayesian perspective. The censored sampling scheme is considered due to its popularity in reliability theory and survival analysis. The expressions for the Bayes estimators and their posterior risks are derived under different loss scenarios. In case, no little prior information is available, elicitation of hyper parameters is given. To examine, numerically, the performance of the Bayes estimators using non-informative and informative priors under different loss functions, we have simulated their statistical properties for different sample sizes and test termination times.</p>

scholarly journals Statistical Analysis of the Mixture of Inverted Exponential Distribution Under Bayesian Approach

2019 ◽  
pp. 1-16
Author(s):  
Tabasam Sultana ◽  
Muhammad Aslam ◽  
Javid Shabbir
Keyword(s):  
Prior Information ◽  
Graphical Representation ◽  
Simulation Analysis ◽  
Real Life ◽  
Type I ◽  
Bayes Estimators ◽  
Exponential Distributions ◽  
Component Mixture ◽  
Real Life Data ◽  
Censored Sampling

This paper is about studying a 3-component mixture of the Inverted Exponential distributions under Bayesian view point. The type-I right censored sampling scheme is considered because of its extensive use in reliability theory and survival analysis. The expressions for the Bayes estimators and their posterior risks are derived under dierent loss scenarios. In case, no or little prior information is available, elicitation of hyper parameters is given. In order to study numerically, the execution of the Bayes estimators under dierent loss functions, their statistical properties have been simulated for dierent sample sizes and test termination times. A real life data example is given to illustrate the study. Graphical representation of the simulation analysis results is also given to study the properties of the Bayes estimators.

scholarly journals Bayes Estimation of Change Point in Discrete Maxwell Distribution

2011 ◽  
Vol 2011 ◽  
pp. 1-8
Author(s):  
Mayuri Pandya ◽  
Hardik Pandya
Keyword(s):  
Change Point ◽  
Prior Information ◽  
Bayes Estimation ◽  
Loss Functions ◽  
Maxwell Distribution ◽  
Bayes Estimators ◽  
Asymmetric Loss ◽  
Bayes Estimates

A sequence of independent lifetimes X1,…,Xm,Xm+1,…,Xn was observed from Maxwell distribution with reliability r1(t) at time t but later, it was found that there was a change in the system at some point of time m and it is reflected in the sequence after Xm by change in reliability r2(t) at time t. The Bayes estimators of m, θ1, θ2 are derived under different asymmetric loss functions. The effects of correct and wrong prior information on the Bayes estimates are studied.

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 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 ON THE BAYESIAN ANALYSIS OF EXTENDED WEIBULL-GEOMETRIC DISTRIBUTION

2019 ◽  
pp. 115-137
Author(s):  
Azeem Ali ◽  
Sajid Ali ◽  
Shama Khaliq
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Geometric Distribution ◽  
Real Life ◽  
Bayes Estimation ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Informative Priors ◽  
Bayes Estimates

The paper deals with the Bayes estimation of Extended Weibull-Geometric (EWG) distribution. In particular, we discuss Bayes estimators and their posterior risks using the noninformative and informative priors under different loss functions. Since the posterior summaries cannot be obtained analytically, we adopt Markov Chain Monte Carlo (MCMC) technique to assess the performance of Bayes estimates for different sample sizes. A real life example is also part of this study.  

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 Bayesian Estimation of the Parameter of the p-Dimensional Size-Biased Rayleigh Distribution

2017 ◽  
Vol 56 (1) ◽  
pp. 88-91
Author(s):  
Arun Kumar Rao ◽  
Himanshu Pandey ◽  
Kusum Lata Singh
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Bayesian Estimation ◽  
Density Function ◽  
Rayleigh Distribution ◽  
Survival Model ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Hazard Functions ◽  
Squared Error

In this paper, we have derived the probability density function of the size-biased p-dimensional Rayleigh distribution and studied its properties. Its suitability as a survival model has been discussed by obtaining its survival and hazard functions. We also discussed Bayesian estimation of the parameter of the size-biased p-dimensional Rayleigh distribution. Bayes estimators have been obtained by taking quasi-prior. The loss functions used are squared error and precautionary.

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