An alternative representation of Altham’s multiplicative-binomial distribution. (English) Zbl 0960.62054

Summary: D.R. Cox [see “The analysis of binary data.” (1970; Zbl 0199.53301)] introduced a log-linear representation for the joint distribution of \(n\) binary-dependent responses. P.M.E. Atham [J. R. Stat. Soc., Ser. C27, 162-167 (1978; Zbl 0438.62008)] derived the distribution of the sum of such responses, under a multiplicative, rather than log-linear, representation and called it multiplicative-binomial. We propose here an alternative form of the multiplicative-binomial, which is derived from the original Cox’s representation and is characterized by intuitively meaningful parameters, and compare its first two moments with those of the standard binomial distribution.


62H05 Characterization and structure theory for multivariate probability distributions; copulas
62E10 Characterization and structure theory of statistical distributions
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[1] Altham, P., Two generalizations of the binomial distribution, App. statist., 27, 162-167, (1978) · Zbl 0438.62008
[2] Cox, D.R., The analysis of multivariate binary data, Appl. statist., 21, 113-120, (1972)
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