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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.

MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas
62E10 Characterization and structure theory of statistical distributions
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References:

[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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