Correlated Binomial Models and Correlation Structures

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.

12 pages, 7 figures

References in corpus (1)

• Evaluation of Tranche in Securitization and Long-range Ising Model

Cited by in corpus (4)

• Finite-size scaling analysis of binary stochastic processes and universality classes of information cascade phase transition
• Infectious Default Model with Recovery and Continuous Limit
• Correlation Structures of Correlated Binomial Models and Implied Default Distribution
• Phase transition of social learning collectives and "Echo chamber"