Bayesian Analysis of Generalized Exponential Distribution

Bayesian estimators of unknown parameters of a two parameter generalized exponential distribution are obtained based on non-informative priors using different loss functions

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

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

Pareto Distribution under Hybrid Censoring: Some Estimation

In the present study, the Pareto model is considered as the model from which observations are to be estimated using a Bayesian approach. Properties of the Bayes estimators for the unknown parameters have studied by using different asymmetric loss functions on hybrid censoring pattern and their risks have compared. The properties of maximum likelihood estimation and approximate confidence length have also been investigated under hybrid censoring. The performances of the procedures are illustrated based on simulated data obtained under the Metropolis-Hastings algorithm and a real data set

Bayesian analysis of exponential Lomax distribution using different loss functions

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Reliability Estimation in Multicomponent Stress-Strength Model Based on Generalized Pareto Distribution

The paper deals with the estimation of multicomponent system reliability where the system has k components with their strengths X1, X2, … Xk being independently and identically distributed random variables and each component is experiencing a random stress Y. The s-out-of-k system is said to function if atleast s out of k (1 ≤ s ≤ k) strength variables exceed the random stress. The reliability of such a system is derived when both strength and stress variables follow generalized Pareto distribution. The system reliability is estimated using maximum likelihood and Bayesian approaches. The maximum likelihood estimators are derived under both simple random sampling and ranked set sampling schemes. Lindley's approximation technique is used to get approximate Bayes estimators. The reliability estimators obtained from both the methods are compared by using mean squares error criteria and real data analysis is carried out to illustrate the procedure

Bayes Estimator of Generalized-Exponential Parameters under Linex Loss Function Using Lindley's Approximation

In this paper, we have obtained the Bayes Estimator of Generalized-Exponential scale and shape parameter using Lindley's approximation (L-approximation) under asymmetric loss functions. The proposed estimators have been compared with the corresponding MLE for their risks based on simulated samples from the Generalized-Exponential distribution