The Inflated-parameter Power Series distributions (IPSD) was introduced in Minkova(2002), as a compound Power Series distributions (PSD) with geometric compounding distribution. The lack of memory property of the geometric distribution leads to some useful properties of the defined family of distributions. In these notes I introduce a bivariate version of the IPSDs. The new family of bivariate distributions is constructed by the trivariate reduction method. The probability mass function, recursion formulas and some properties are given. The particular cases of bivariate I-Poisson, I-binomial and I-negative binomial distributions are analyzed in detail.

Minkova L.D. (2002). A generalization of the classical discrete distributions, Communications in Statistics: Theory and Methods, 31, 871-888.