Abstract
The conditional distribution of Y given X=x, where X and Y are non-negative integer-valued random variables, is characterized in terms of the regression function of X on Y and the marginal distribution of X which is assumed to be of a power series form. Characterizations are given for a binomial conditional distribution when X follows a Poisson, binomial or negative binomial, for a hypergeometric conditional distribution when X is binomial and for a negative hypergeometric conditional distribution when X follows a negative binomial.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Cacoullos, T. and Papageorgiou, H. (1983). Characterizations of discrete distributions by a conditional distribution and a regression function, Ann. Inst. Statist. Math., 35, 95–103.
Cacoullos, T. and Papageorgiou, H. (1984). Characterizations of mixtures of continuous distributions by their posterior means, Scand. Actuar. J., 23–30.
Dahiya, R. C. and Korwar, R. M. (1977). On characterizing some bivariate discrete distributions by linear regression, Sankhyā Ser. A, 39, 124–129.
David, F. N. and Barton, D. E. (1962). Combinatorial Chance, Griffin, London.
Kendall, M. G. and Stuart, A. (1969). The Advanced Theory of Statistics, Vol. 1, Distribution Theory, Griffin, London.
Khatri, C. G. (1978a). Characterization of some discrete distributions by linear regression, J. Indian Statist. Assoc., 16, 49–58.
Khatri, C. G. (1978b). Characterization of some multivariate distributions by conditional distributions and linear regression, J. Indian Statist. Assoc., 16, 59–70.
Korwar, R. M. (1975). On characterizing some discrete distributions by linear regression, Comm. Statist., 4, 1133–1147.
Kyriakoussis, A. (1988). Characterization of bivariate discrete distributions, Sankhyā Ser. A, 50, 286–287.
Papageorgiou, H. (1983). On characterizing some bivariate discrete distributions, Austral. J. Statist., 25, 136–144.
Papageorgiou, H. (1983). Characterizations of multinomial and negative multinomial mixtures by regression, Austral. J. Statist., 26, 25–29.
Papageorgiou, H. (1985). On characterizing some discrete distributions by a conditional distribution and a regression function, Biometrical J., 27, 473–479.
Author information
Authors and Affiliations
About this article
Cite this article
Kyriakoussis, A., Papageorgiou, H. On characterization of power series distributions by a marginal distribution and a regression function. Ann Inst Stat Math 41, 671–676 (1989). https://doi.org/10.1007/BF00057733
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00057733