Abstract
The main object of this article is the estimation of the unknown population parameters and the reliability function for the generalized Bilal model under type-II censored data. Both maximum likelihood and Bayesian estimates are considered. In the Bayesian framework, although we have discussed mainly the squared error loss function, any other loss function can easily be considered. Gibb’s sampling procedure is used to draw Markov Chain Monte Carlo (MCMC) samples, which have been used to compute the Bayes estimates and also to construct their corresponding credible intervals with the help of two different importance sampling techniques. A simulation study is carried out to examine the accuracy of the resulting Bayesian estimates and compare them with their corresponding maximum likelihood estimates. Application to a real data set is considered for the sake of illustration.
Highlights
The generalized Bilal (GB) model coincides with the distribution of the median in a sample of size three from the Weibull distribution
The GB model can be used for several practical data analysis
2) The Bayes estimators under prior 1 or prior 2 by using Second importance sampling technique (IS2) technique are mainly better than the corresponding estimators by using First importance sampling technique (IS1) technique in terms of in terms of average bias and Mean squared error (MSE). 3) In all cases, the MSEs of the maximum likelihood estimate (MLE) are less than the corresponding Bayes estimators under prior 1 by using IS1 technique
Summary
The generalized Bilal (GB) model coincides with the distribution of the median in a sample of size three from the Weibull distribution. Maximum likelihood estimation It follows from (1) and (3) that, based on a given type-II censored sample x drawn from the GB distribution, the joint PDF of the papulation parameters β and λ is given by: L(β, λ|x) ∝ βrλr e−2 β T1+T2 , (6) Remark 2 An initial value for λ, λ (M0), can be obtained as follows: (1) Calculate the sample coefficient of variation (CV) based on a given type-II censored sample data as if it is complete.
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