Empirical Bayes Estimators of Parameter and Reliability Function for Compound Rayleigh Distribution under Record Data.

Younis²,

Alkhedir³

2016

<p>This paper aims to introduce a comparative study for the E-Bayesian criteria with three various Bayesian approaches; Bayesian, hierarchical Bayesian and empirical Bayesian. This study is concerned to estimate the shape parameter and the hazard function of the Gompertz distribution based on type-II censoring. All estimators are obtained under symmetric loss function [squared error loss (SELF))] and three different asymmetric loss functions [quadratic loss function (QLF), entropy loss function (ELF) and LINEX loss function (LLF)]. Comparisons among all estimators are achieved in terms of mean square error (MSE) via Monte Carlo simulation.</p>

Section: Empirical Bayesian Estimationmentioning

confidence: 99%

Comparison of estimates using censored samples from Gompertz model: Bayesian, E-Bayesian, hierarchical Bayesian and empirical Bayesian schemes

Younis²,

Alkhedir³

2016

“…The Bayes approach assumed that the hyper parameter a is known. When a is unknown, we may use the empirical Bayes criteria to get its estimates from the likelihood function and probability density function of the prior distribution [33].Now, from (2-7) and (2-9), the marginal distribution of x given a is obtained as:…”

Section: The Quasi-empirical Bayesian Estimationmentioning

confidence: 99%

Quasi-E-Bayesian criteria versus quasi-Bayesian, quasi-hierarchical Bayesian and quasi-empirical Bayesian methods for estimating the scale parameter of the Erlang distribution

Younis

Alkhedir

2016

This paper proposes a new modification for the E-Bayesian method of estimation to introduce a new technique namely Quasi E-Bayesian method (or briefly QE-Bayesian). The suggested criteria built in replacing the likelihood function by the quasi likelihood function in the E-Bayesian technique. This study is devoted to evaluate the performance of the new method versus the quasi-Bayesian, quasihierarchical Bayesian and quasi-empirical Bayesian approaches in estimating the scale parameter of the Erlang distribution.

“…Abushal [1] applied the maximum likelihood and Bayes approaches to estimate parameters, reliability and hazard functions of the CR distribution based on progressive first-failure censoed data. Shajaee et al [2] obtained the empirical Bayes estimates for parameter and reliability function associated with the CR distribution under record data. Barot and Patal [3] compared the maximum likelihood and Bayes estimates of the reliability parameters corresponding to the CR distribution under progressive type-ii censored data.…”

Section: Introductionmentioning

confidence: 99%

The beta compound Rayleigh distribution : Properties and applications

Ibrahim

2017

In this paper, we introduce a new four parameter continuous model, called the beta compound Rayleigh (BCR) distribution that extends the compound Rayleigh distribution. Basic properties of the proposed distribution such as; mean, variance, coefficient of variation, raw and incomplete moments, skewness, kurtosis, moment and probability generating functions, reliability analysis, Lorenz, Bonferroni and Zenga curves, Rényi of entropy, order statistics and record statistics are investigated. We obtain the maximum likelihood estimates and the observed information matrix for the model parameters. Two real data sets are used to illustrate the usefulness of the new model.