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A Simple Distribution for the Sum of Correlated, Exchangeable Binary Data

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  • Gary Witt

Abstract

This article describes a generalization of the binomial distribution. The closed form probability function for the probability of k successes out of n correlated, exchangeable Bernoulli trials depends on the number of trials and its two parameters: the common success probability and the common correlation. The distribution is derived under the assumption that the common correlation between all pairs of Bernoulli trials remains unchanged conditional on successes in all completed trials. The distribution was developed to model bond defaults but may be suited to biostatistical applications involving clusters of binary data encountered in repeated measurements or toxicity studies of families of organisms. Maximum likelihood estimates for the parameters of the distribution are found for a set of binary data from a developmental toxicity study on litters of mice.

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  • Gary Witt, 2014. "A Simple Distribution for the Sum of Correlated, Exchangeable Binary Data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(20), pages 4265-4280, October.
    • Handle: RePEc:taf:lstaxx:v:43:y:2014:i:20:p:4265-4280
    DOI: 10.1080/03610926.2012.725148
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    Cited by:

    1. Henry Penikas, 2023. "IRB Asset and Default Correlation: Rationale for the Macroprudential Mark-Ups to the IRB Risk-Weights," Risk Management, Palgrave Macmillan, vol. 25(1), pages 1-27, March.
    2. Dmitriy Borzykh & Henry Penikas, 2021. "IRB PD model accuracy validation in the presence of default correlation: a twin confidence interval approach," Risk Management, Palgrave Macmillan, vol. 23(4), pages 282-300, December.
    3. Henry Penikas, 2020. "IRB Asset and Default Correlation: Rationale for the Macroprudential Add-ons to the Risk-Weights," Bank of Russia Working Paper Series wps56, Bank of Russia.
    4. Cesa-Bianchi, Ambrogio & Eguren Martin, Fernando & Thwaites, Gregory, 2019. "Foreign booms, domestic busts: The global dimension of banking crises," Journal of Financial Intermediation, Elsevier, vol. 37(C), pages 58-74.

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