On characterizing some discrete distributions by linear regression

Abstract

The binomial, negative binomial (and hence geometric) and pisson distributions are characterized, in the context of some well-known bivariate distributions, by the conditional distributionof one random variable (r.v.) given another, and the linear regression of the second, r.v. on the first. The conditional distribution. of the first r.v. given the second is also characterized by each of three sets of conditions.

Keywords:

• binomial
• bivariate
• geometric
• negavive binomial and poisson distribution
• characterizations
• linear regression