Sampling from a couple of positively correlated binomial variables

TL;DR

This paper explores how to construct positively correlated binomial variables from multinomial marginals, analyzing parameter restrictions and the properties of their regression functions.

Contribution

It introduces methods to generate positively correlated binomial variables from multinomial marginals and examines the conditions and regression characteristics involved.

Findings

Positive correlation can be achieved through specific linear combinations.

Parameter restrictions are necessary for positive correlation.

Regression function is linear but not homoscedastic.

Abstract

We know that the marginals in a multinomial distribution are binomial variates exhibiting a negative correlation. But we can construct two linear combinations of such marginals in such a way to obtain a positive correlation. We discuss the restrictions that are to be imposed on the parameters of the given marginals to accomplish such a result. Next we discuss the regression function, showing that it is a linear function but not homoscedastic.