Title: On Bivariate Discrete Weibull Distribution,
Abstract: Recently, Lee and Cha (2015, `On two generalized classes of discrete
bivariate distributions', {\it American Statistician}, 221 - 230) proposed two
general classes of discrete bivariate distributions. They have discussed some
general properties and some specific cases of their proposed distributions. In
this paper we have considered one model, namely bivariate discrete Weibull
distribution, which has not been considered in the literature yet. The proposed
bivariate discrete Weibull distribution is a discrete analogue of the
Marshall-Olkin bivariate Weibull distribution. We study various properties of
the proposed distribution and discuss its interesting physical interpretations.
The proposed model has four parameters, and because of that it is a very
flexible distribution. The maximum likelihood estimators of the parameters
cannot be obtained in closed forms, and we have proposed a very efficient
nested EM algorithm which works quite well for discrete data. We have also
proposed augmented Gibbs sampling procedure to compute Bayes estimates of the
unknown parameters based on a very flexible set of priors. Two data sets have
been analyzed to show how the proposed model and the method work in practice.
We will see that the performances are quite satisfactory. Finally, we conclude
the paper.