Sums of possibly associated multivariate indicator functions: the Conway-Maxwell-multinomial distribution. (English) Zbl 1398.62128

Summary: The Conway-Maxwell-Multinomial distribution is studied in this paper. Its properties are demonstrated, including sufficient statistics and conditions for the propriety of posterior distributions derived from it. An application is given using data from Mendel’s ground-breaking genetic studies.


62H05 Characterization and structure theory for multivariate probability distributions; copulas
60E05 Probability distributions: general theory
62P10 Applications of statistics to biology and medical sciences; meta analysis
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[1] Boatwright, P., Borle, S. and Kadane, J. B. (2003). A model of the joint distribution of purchase quantity and timing. J. Amer. Statist. Assoc.98, 564-572. · Zbl 1045.62118
[2] Borle, S., Boatwright, P., Kadane, J. B., Nunes, J. C. and Shmueli, G. (2005). The effect of product assortment changes on customer retention. Mark. Sci.4, 616-622.
[3] Conway, R. and Maxwell, W. (1962). A queing model with state dependent service rates. J. Ind. Eng.12, 132-136.
[4] Diaconis, P. and Ylvisaker, D. (1979). Conjugate priors for exponential families. Ann. Statist.7, 269-281. · Zbl 0405.62011
[5] Fisher, R. A. (1936). Has Mendel’s work been rediscovered? Ann. of Sci.1, 115-137.
[6] Fisher, R. A. (1959). Statistical Methods and Scientific Inference, 2nd ed. Edinburgh: Oliver and Boyd.
[7] Franklin, A., Edwards, A. W. F., Fairbanks, D. J., Hartl, D. L. and Seidenfeld, T. (2008). Ending the Mendel-Fisher Controversy. Pittsburgh: University of Pittsburgh Press.
[8] Kadane, J. B. (2016). Sums of possibly associated Bernoulli variables: The Conway-Maxwell-Binomial distribution. Bayesian Anal.11, 403-420. · Zbl 1357.60019
[9] Pires, A. M. and Branco, J. A. (2010). A statistical model to explain the Mendel-Fisher controversy. Statist. Sci.25, 545-565. · Zbl 1329.62094
[10] Shmueli, G., Minka, T. P., Kadane, J. B., Borle, S. and Boatwright, P. (2004). A useful distribution for fitting discrete data: Revival of the COM-Poisson. J. R. Stat. Soc., Ser. C, Appl. Stat.54, 127-142. · Zbl 1490.62058
[11] Weldon, W. R. F. (1902). Mendel’s law of alternative inference in peas.
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