Limit theorems for the Multiplicative Binomial Distribution (MBD)

Abstract

The sum of $n$ {non-independent} Bernoulli random variables could be modeled in several different ways. One of these is the Multiplicative Binomial Distribution (MBD), introduced by Altham (1978) and revised by Lovison (1998). In this work, we focus on the distribution asymptotic behavior as its parameters diverge. In addition, we derive a specific property describing the relationship between the joint probability of success of $n$ binary-dependent responses and the individual Bernoulli one; particularly, we prove that it depends on both the sign and the strength of the association between the random variables.