No abstract

No abstract

No 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.

In this paper, finite mixture of two exponentiated Weibull distributions is suggested. We show that this proposed model may have bathtub shaped, bathtub-constant shaped, increasing or decreasing failure rate functions. Therefore, this model may be utilized for various applications in practices. The problem of identifiability of finite mixture of exponentiated Weibull distributions is studied. The maximum likelihood estimates (MLE's) of the parameters of this proposed model is provided, where an iterative procedure is presented for this purpose. Through Monte Carlo simulation experiments, we show the consistency of the resulting estimators via the root mean squared errors (RMSE's) for various combination of the population parameters. Applications to two real data sets are studied. Finally, some concluding remarks are presented.