On some properties and applications of bivariate generalized geometric distribution

Here we introduce a bivariate version of the generalized geometric distribution of Kumar and Harisankar (Jour. Statistist. Comput. Simul., 2020) through the name, the bivariate generalized geometric distribution (BGGD), which we obtained as the distribution of the random sum of certain types of independent and identically distributed bivariate Bernoulli random variables. A genesis of the distribution and explicit closed form expressions for its probability mass function, factorial moments and the p.g.f.’s of its conditional distributions and marginal distribution are derived. Certain recurrence relations for probabilities, raw moments and factorial moments of the BGGD are also obtained. The method of maximum likelihood estimation is employed for estimating the parameters of the distribution. A Monte Carlo simulation study empirically evaluates and compares the performance of the proposed estimators in terms of bias and standard error. 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.