Correlated Binomial Models and Correlation Structures

by Masato Hisakado of Standard & Poor's,
Kenji Kitsukawa of Keio University, and
Shintaro Mori of Kitasato University

May 22, 2006  {These authors have stamped a new date on this paper most every month since its inception, but ( strangely ) the content never changes. I'm weary of this game and have fixed its date at its inception.
All other papers on this site are stamped with the date of their current version.}

Abstract: We discuss a general method to construct correlated binomial distributions by imposing several consistent relations on the joint probability function. We obtain self-consistency relations for the conditional correlations and conditional probabilities. The beta-binomial distribution is derived by a strong symmetric assumption on the conditional correlations. Our derivation clarifies the 'correlation' structure of the beta-binomial distribution. It is also possible to study the correlation structures of other probability distributions of exchangeable (homogeneous) correlated Bernoulli random variables. We study some distribution functions and discuss their behaviors in terms of their correlation structures.

PACS: 02.50.Cw.

Keywords: CDO, Correlated Binomial.

Published in: Journal of Physics A: Mathematical and General, Vol. 39, No. 50, (December 2006), pp. 15365-15378.

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