DISCRETE DISTRIBUTIONS CONNECTED WITH THE BIVARIATE BINOMIAL

Year 2010, Volume: 39 Issue: 1, 109 - 120, 01.01.2010

İ. Bairamov O. Elmastas Gultekin

Abstract

DISCRETE DISTRIBUTIONS CONNECTED WITH THE BIVARIATE BINOMIAL

Abstract

A new class of multivariate discrete distributions with binomial and multinomial marginals is studied. This class of distributions is obtained in a natural manner using probabilistic properties of the sampling model considered. Some possible applications in game theory, life testing and exceedance models for order statistics are discussed.

Keywords

Discrete multivariate distributions, Bivariate binomial distribution, Multinomial distribution, Probability density function, Poisson approximation, 2000 AMS Classification: 62 E 15

References

• Aitken, A. C. and Gonin, H. T. On fourfold sampling with and without replacement, Proc. Roy. Soc. Edinburgh 55, 114–125, 1935.
• Bairamov I. and Kotz. S. On local dependence function for multivariate distributions, New Trends in Probability and Statistics 5, 27–44, 2000.
• Bairamov I. G., Kotz S. and Kozubowski T. A new measure on linear local dependence, Statistics, 37 (3), 243–258, 2003.
• Biswasa, A. and Hwang, J. S. A new bivariate binomial distribution, Statistics and Proba- bility Letters 60, 231–240, 2002.
• Bjerve, S. and Doksum, K. Correlation curves: measures of association as functions of covariate values, Ann. Statist. 21, 890–902, 1993.
• Chandrasekar, B. and Balakrishnan N. Some properties and a characterization of trivariate and multivariate binomial distributions, Statistics 36, 211–218, 2002.
• David H. A. Concomitant of order statistics, Theory and Application, in: Krishnaiah, P, R., Sen, P. K. (Eds.) (Handbook of Statistics 4, North-Holland, Amsterdam, 1993), 383–403.
• Doss, D. C. and Graham, R. C. A characterization of multinomial bivariate distribution by univariate marginals, Bull. Calcutta Statist. Assoc. 24, 93–99, 1975.
• Eryilmaz, S. and Bairamov, I. G. On a new sample rank of an order statistic and its con- comitant, Statist. Probab. Lett. 63, 123–131, 2003.
• Hamdan, M. A. Canonical expansions of the bivariate binomial distribution with unequal marginal indices, Int. Statist. Rev. 40, 277–280, 1972.
• Hamdan, M. A. A note on the trinomial distribution, Int. Statist. Rev. 43, 219–220, 1975.
• Hamdan, M. A. and Al-Bayati, H. A. A note on the bivariate Poisson distribution, Amer. Statist. 23, 32–33, 1969.
• Hamdan, M. A. and Jensen, D. R. A bivariate binomial distribution and some applications, Austral. J. Statist. 18, 163–169, 1976.
• Jones M. C. The local dependence function, Biometrika 83, 899–904, 1996.
• Johnson N. L., Kotz S. and Balakrishnan N. Discrete Multivariate Distributions (John Wiley & Sons, New York, 1997).
• Kocherlakota, S. and Kocherlakota, K. Bivariate Discrete Distributions (Marcel Dekker, New York, 1992).
• Krishnamoorthy, A. S. Multivariate Poisson and binomial distributions, Sankhya 11, 117– , 1951.
• Kotz, S. and Nadarajah, S. Local dependence functions for the elliptically symmetric dis- tributions, Sankhya 65 (1), 207–223, 2003.
• Papageorgiou, H. and David, K. M. On countable mixtures of bivariate binomial distribu- tions, Biom. J. 36, 581–601, 1994.
• Papageorgiou, H. and David, K. M. The structure of compounded trivariate binomial distri- butions, Biom. J. 37, 81–95, 1995.
• Shanbhag, D. N. and Basawa, I. V. (1974). On a characterization property of multinomial distribution, Trab. Estad. 25, 109–112, 1974.
• Voinov, V. and Nikulin, M. Unbiased Estimators and their Applications 2: Multivariate case(Kluwer, 1996).
• Voinov, V., Nikulin, M. and Smirnov, T. Multivariate discrete distributions induced by an urn scheme, linear diophantine equations, unbiased estimating and testing, J. Statist. Plann. Inference 101 (1-2), 255–266, 2002.