Marshall-Olkin type bivariate distributions with bounded domain

Bivariate distributions appropriate for modeling various data sets have been proposed to model simultaneous events in statistical reliability theory. In particular, Marshall-Olkin-type bivariate distributions can model bivariate data containing both inequality and equality cases in that they contain continuous and singular parts. Generalization of Marshall-Olkin type bivariate distributions, which are generally defined on (0, ∞), to a bounded domain is important in modeling proportional data. In this thesis, a Marshall-Olkin-type bivariate generalization of a special case of the omega distribution, which is in the class of distributions with a bounded domain, is defined. Maximum likelihood estimates of the parameters of this distribution are obtained and an EM algorithm and a Bayesian estimation method are proposed for parameter estimation. Several properties of the distribution, such as marginal distributions, joint survival function and product moments are analyzed in detail. Moreover, the performance of the estimators of the parameters from the proposed distribution is investigated through simulation studies and real data analyzes. The new distribution is found to be a useful alternative distribution for modeling bivariate proportional data.