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 Bayes Estimation of Two-Phase Linear Regression Model

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Mayuri Pandya ◽  
Krishnam Bhatt ◽  
Paresh Andharia
Keyword(s):  
Regression Model ◽  
Change Point ◽  
Prior Information ◽  
Bayes Estimation ◽  
Loss Functions ◽  
Random Errors ◽  
Two Phase ◽  
Inference Problem ◽  
Bayes Estimates ◽  
Linex Loss

Let the regression model be Yi=β1Xi+εi, where εi are i. i. d. N (0,σ2) random errors with variance σ2>0 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 slope, regression parameter β2. The problem of study is when and where this change has started occurring. This is called change point inference problem. The estimators of m, β1,β2 are derived under asymmetric loss functions, namely, Linex loss & General Entropy loss functions. The effects of correct and wrong prior information on the Bayes estimates are studied.

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 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 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 Approximate Bayes Estimators of the Parameters of the Inverse Gaussian Distribution Under Different Loss Functions

2020 ◽  
Author(s):  
Ilhan Usta ◽  
Merve Akdede
Keyword(s):  
Gaussian Distribution ◽  
Inverse Gaussian Distribution ◽  
Loss Functions ◽  
Approximation Methods ◽  
Inverse Gaussian ◽  
Bayes Estimators ◽  
Unknown Parameters ◽  
Data Set ◽  
Bayes Estimates ◽  
Two Parameters

Inverse Gaussian is a popular distribution especially in the reliability and life time modelling, and thus the estimation of its unknown parameters has received considerable interest. This paper aims to obtain the Bayes estimators for the two parameters of the inverse Gaussian distribution under varied loss functions (squared error, general entropy and linear exponential). In Bayesian procedure, we consider commonly used non-informative priors such as the vague and Jeffrey’s priors, and also propose using the extension of Jeffrey’s prior. In the case where the two parameters are unknown, the Bayes estimators cannot be obtained in the closed-form. Hence, we employ two approximation methods, namely Lindley and Tierney Kadane (TK) approximations, to attain the Bayes estimates of the parameters. In this paper. the effects of considered loss functions, priors and approximation methods on Bayesian parameter estimation are also presented. The performance of Bayes estimates is compared with the corresponding classical estimates in terms of the bias and the relative efficiency throughout an extensive simulation study. The results of the comparison show that Bayes estimators obtained by TK method under linear exponential loss function using the proposed prior outperform the other estimators for estimating the parameters of inverse Gaussian distribution most of the time. Finally, a real data set is provided to illustrate the results.

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.

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 Bayes Estimation Under Different Censoring Patterns On Constant-Stress PALT

2018 ◽  
Vol 47 (4) ◽  
pp. 60-74
Author(s):  
Gyan Prakash
Keyword(s):  
Bayes Estimation ◽  
Constant Stress ◽  
Accelerated Life Test ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Life Test ◽  
Gompertz Distribution ◽  
Accelerated Life ◽  
Special Cases ◽  
Two Parameter

Two-Parameter Gompertz distribution is considered here for the Bayesian inference under the Constant-Stress Partially Accelerated Life Test (CS-PALT). The first-failure Progressive (FFP) censoring pattern and its special cases have used for the analysis based on Bayes estimators of all the parameters under two different asymmetric loss functions and their special cases. A simulation study has carried out for the numerical analysis.

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