Abstract
Here we introduce a bivariate generalized hypergeometric factorial moment distribution (BGHFMD) through its probability generating function (p.g.f.) whose marginal distributions are the generalized hypergeometric factorial moment distributions introduced by Kemp and Kemp (Bull Int Stat Inst 43:336–338,1969). Well-known bivariate versions of distributions such as binomial, negative binomial and Poisson are special cases of this distribution. A genesis of the distribution and explicit closed form expressions for the probability mass function of the BGHFMD, its factorial moments and the p.g.f.’s of its conditional distributions are derived here. Certain recurrence relations for probabilities, moments and factorial moments of the bivariate distribution are also established.
Similar content being viewed by others
References
Johnson NL, Kotz S, Kemp AW (1992) Univariate discrete distributions. Wiley, New York
Kemp AW, Kemp CD (1974) A family of discrete distributions defined via their factorial moments. Commun in Stati Theory Methods 3:1187-1196
Kemp CD, Kemp AW (1969) Some distributions arising from an inventory decision problem. Bull Inte Stat Ins 43:336-338
Kocherlakota S, Kocherlakota K (1992) Bivariate discrete distributions. Marcel Dekker, New York
Kumar CS, Moothathu TSK (2000) Generalized hypergeometric factorial moment distribution of order k. Calcutta Stat Assoc Bull 50:71-78
Mathai AM, Saxena RK (1973) Generalized hypergeometric functions with applications in statistics and physical sciences. Lecture notes No. 348. Springer, Heidelberg
Moothathu TSK, Kumar CS(1997) On bivariate generalized hypergeometric probability distributions. J Indian Stat Assoc 35:51-59
Piperigou VE, Papageorgiou H (2003) On bivariate discrete distributions: a unified treatment. Metrika 58:221-233
Slater LJ (1966) Generalized hypergeometric functions. Cambridge University Press, Cambridge
Subrahmaniam K (1966) A test for ‘intrinsic correlation’ in the theory of accident proneness. J Roy Stat Soc Ser B 28:180-189
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Satheesh Kumar, C. A unified approach to bivariate discrete distributions. Metrika 67, 113–123 (2008). https://doi.org/10.1007/s00184-007-0125-8
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00184-007-0125-8