A Distribution for the Sum of Correlated Bernoulli Trials

• Activity Number: 44
• Type: Contributed
• Date/Time: Sunday, August 1, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Gary Witt*+
• Companies: Temple University
• Keywords: Correlated Bernoulli Trials

Abstract

This paper describes a generalization of the binomial distribution that has been used to model defaults in portfolios of correlated bonds. The closed form distribution function for the probability of k successes out of n correlated, exchangeable Bernoulli trials depends on its three parameters: the number of trials, the common default probability and the common correlation. The distribution is derived from the assumption that the common correlation between all pairs of Bernoulli trials remains unchanged conditional on successes in all completed trials. The distribution may be suited to biostatical applications involving clusters of binary data as are often encountered in repeated measurements or toxicology studies of families of organisms.