In this paper we consider the Marshall-Olkin bivariate Weibull distribution. The Marshall-Olkin bivariate Weibull distribution is a singular distribution, whose both the marginals are univariate Weibull distributions. This is a generalization of the Marshall-Olkin bivariate exponential distribution. The cumulative joint distribution of the Marshall-Olkin bivariate Weibull distribution is a mixture of an absolute continuous distribution function and a singular distribution function. This distribution has four unknown parameters and it is observed that the maximum likelihood estimators of the unknown parameters can not be obtained in explicit forms. In this paper we discuss about the computation of the maximum likelihood estimators of the unknown parameters using EM algorithm. We perform some simulations to see the performances of the EM algorithm and re-analyze one data set for illustrative purpose.

In this paper we consider the model selection/ discrimination among the three important lifetime distributions. All these three distributions have been used quite effectively to analyze lifetime data in the reliability analysis. We study the probability of correct selection using the maximized likelihood method, as it has been used in the literature. We further compute the asymptotic probability of correct selection and compare the theoretical and simulation results for different sample sizes and for different model parameters. The results have been extended for Type-I censored data also. The theoretical and simulation results match quite well. Two real data sets have been analyzed for illustrative purposes. We also suggest a method to determine the minimum sample size required to discriminate among the three distributions for a given probability of correct selection and a user specified protection level.

Log-normal and log-logistic distributions are often used to analyze lifetime data. For certain ranges of the parameters, the shape of the probability density functions or the hazard functions can be very similar in nature. It might be very difficult to discriminate between the two distribution functions. In this paper, we consider the discrimination procedure between the two distribution functions. We use the ratio of maximized likelihood for discrimination purposes. The asymptotic properties of the proposed criterion have been investigated. It is observed that the asymptotic distributions are independent of the unknown parameters. The asymptotic distributions have been used to determine the minimum sample size needed to discriminate between these two distribution functions for a user specified probability of correct selection. We have performed some simulation experiments to see how the asymptotic results work for small sizes. For illustrative purpose two data sets have been analyzed.

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