Limit theorems for the Multiplicative Binomial Distribution (MBD)
Francesca Fortunato

TL;DR
This paper investigates the asymptotic behavior of the Multiplicative Binomial Distribution (MBD) for diverging parameters and explores how the joint success probability relates to individual Bernoulli responses based on their association.
Contribution
It provides new theoretical insights into the asymptotic properties of the MBD and characterizes the influence of dependence structure on joint success probabilities.
Findings
Asymptotic behavior of MBD as parameters diverge
Relationship between joint and individual success probabilities
Dependence on sign and strength of association
Abstract
The sum of {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 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.
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Taxonomy
TopicsStatistical Distribution Estimation and Applications · Statistical Methods and Bayesian Inference · Advanced Statistical Methods and Models
