Hostname: page-component-8448b6f56d-c47g7 Total loading time: 0 Render date: 2024-04-18T23:03:48.660Z Has data issue: false hasContentIssue false
  • English
  • Français

On characterizing the Pólya distribution

Published online by Cambridge University Press:  15 November 2002

Héctor M. Ramos ,
David Almorza  and
Juan A. García–Ramos
Héctor M. Ramos
Affiliation:
Departamento de Estadística e Investigación Ope ra ti va, Facultad de Ciencias Económicas y Empresariales, Universidad de Cádiz, c/Duque de Nájera 8, 11002 Cádiz, Spain; hector.ramos@uca.es.
David Almorza
Affiliation:
Departamento de Estadística e Investigación Ope ra ti va, Facultad de Ciencias Económicas y Empresariales, Universidad de Cádiz, c/Duque de Nájera 8, 11002 Cádiz, Spain;
Juan A. García–Ramos
Affiliation:
Departamento de Estadística e Investigación Ope ra ti va, Facultad de Ciencias Económicas y Empresariales, Universidad de Cádiz, c/Duque de Nájera 8, 11002 Cádiz, Spain;
Get access

Abstract

In this paper two characterizations of the Pólya distribution are obtained when its contagion parameter is negative. One of them is based on mixtures and the other one is obtained by characterizing a subfamily of the discrete Pearson system.

Keywords

Pólya distributionhypergeometric distributioncharacterization.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 6: New directions in Time Series Analysis (Guest Editor: Philippe Soulier)New directions in Time Series Analysis (Guest Editor: Philippe Soulier) , 2002 , pp. 105 - 112
Copyright
© EDP Sciences, SMAI, 2002

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bosch, A.J., The Pólya distribution. Statist. Neerlandica 17 (1963) 201-213. CrossRef
Eggenberger, F. and Pólya, G., Über die Statistik Verketteter Vorgänge. Z. Angew. Math. Mech. 3 (1923) 279-289. CrossRef
Eggenberger, F. and Pólya, G., Calcul des probabilités - sur l'interprétation de certaines courbes de fréquence. C. R. Acad. Sci. Paris 187 (1928) 870-872.
Feller, W., On a general class of ``contagious" distributions. Ann. Math. Statist. 14 (1943) 389-400. CrossRef
Friedman, B., A simple urn model. Comm. Pure Appl. Math. 2 (1949) 59-70. CrossRef
Hald, A., The compound hypergeometric distribution and a system of single sampling inspection plans based on prior distributions and costs. Technometrics 2 (1960) 275-340. CrossRef
Janardan, K.G., Characterizing, On the Markov-Pólya distribution. Sankhya Ser. A 46 (1984) 444-453.
Janardan, K.G. and Schaeffer, D.J., A generalization of Markov-Pólya distribution its extensions and applications. Biometrical J. 19 (1977) 87-106. CrossRef
N.L. Johnson and S. Kotz, Urn Models and Their Application. Wiley, New York (1977).
Jordan, C., Sur un cas généralisé de la probabilité des épreuves répétées. C. R. Acad. Sci. Paris 184 (1927) 315-317.
Ollero, J. and Ramos, H.M., Description of a Subfamily of the Discrete Pearson System as Generalized-Binomial Distributions. J. Italian Statist. Soc. 2 (1995) 235-249. CrossRef
Ord, J.K., On a System of Discrete Distributions. Biometrika 54 (1967) 649-656.
J.K. Ord, Families of Frequency Distributions. Griffin, London (1972).
Panaretos, J. and Xekalaki, E., On some distributions arising from certain generalized sampling schemes. Commun. Statist. Theory Meth. 15 (1986) 873-891. CrossRef
Panaretos, J. and Xekalaki, E., A probability distribution associated with events with multiple occurrences. Statist. Probab. Lett. 8 (1989) 389-396. CrossRef
G.P. Patil and S.W. Joshi, A Dictionary and Bibliography of Discrete Distributions. Oliver & Boyd, Edinburgh (1968).
Philippou, A.N., Tripsiannis, G.A. and Antzoulakos, D.L., New Pólya and inverse Pólya distributions of order k. Commun. Statist. Theory Meth. 18 (1989) 2125-2137. CrossRef
Pólya, G., Sur quelques points de la théorie des probabilités. Ann. Inst. H. Poincaré 1 (1930) 117-161.
Skibinsky, M., A characterization of hypergeometric distributions. J. Amer. Statist. Assoc. 65 (1970) 926-929. CrossRef