Brazilian Journal of Probability and Statistics

Sums of possibly associated multivariate indicator functions: The Conway–Maxwell-Multinomial distribution

Joseph B. Kadane and Zhi Wang

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Abstract

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.

Article information

Source
Braz. J. Probab. Stat., Volume 32, Number 3 (2018), 583-596.

Dates
Received: July 2016
Accepted: February 2017
First available in Project Euclid: 8 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1528444873

Digital Object Identifier
doi:10.1214/17-BJPS355

Mathematical Reviews number (MathSciNet)
MR3812383

Zentralblatt MATH identifier
06930040

Keywords
Conjugate prior distributions proper prior distributions natural exponential family

Citation

Kadane, Joseph B.; Wang, Zhi. Sums of possibly associated multivariate indicator functions: The Conway–Maxwell-Multinomial distribution. Braz. J. Probab. Stat. 32 (2018), no. 3, 583--596. doi:10.1214/17-BJPS355. https://projecteuclid.org/euclid.bjps/1528444873


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References

  • 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.
  • 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.
  • Conway, R. and Maxwell, W. (1962). A queing model with state dependent service rates. J. Ind. Eng. 12, 132–136.
  • Diaconis, P. and Ylvisaker, D. (1979). Conjugate priors for exponential families. Ann. Statist. 7, 269–281.
  • Fisher, R. A. (1936). Has Mendel’s work been rediscovered? Ann. of Sci. 1, 115–137.
  • Fisher, R. A. (1959). Statistical Methods and Scientific Inference, 2nd ed. Edinburgh: Oliver and Boyd.
  • 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.
  • Kadane, J. B. (2016). Sums of possibly associated Bernoulli variables: The Conway–Maxwell-Binomial distribution. Bayesian Anal. 11, 403–420.
  • Pires, A. M. and Branco, J. A. (2010). A statistical model to explain the Mendel–Fisher controversy. Statist. Sci. 25, 545–565.
  • 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.
  • Weldon, W. R. F. (1902). Mendel’s law of alternative inference in peas. Biometrika 1, 228–254.