On characterizing the Pólya distribution
ESAIM: Probability and Statistics, Tome 6 (2002), pp. 105-112.

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.

DOI : 10.1051/ps:2002005
Classification : 60E05, 60E99
Mots-clés : Pólya distribution, hypergeometric distribution, characterization
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Ramos, Héctor M.; Almorza, David; García-Ramos, Juan A. On characterizing the Pólya distribution. ESAIM: Probability and Statistics, Tome 6 (2002), pp. 105-112. doi : 10.1051/ps:2002005. http://archive.numdam.org/articles/10.1051/ps:2002005/

[1] A.J. Bosch, The Pólya distribution. Statist. Neerlandica 17 (1963) 201-213.

[2] F. Eggenberger and G. Pólya, Über die Statistik Verketteter Vorgänge. Z. Angew. Math. Mech. 3 (1923) 279-289. | JFM

[3] F. Eggenberger and G. Pólya, Calcul des probabilités - sur l'interprétation de certaines courbes de fréquence. C. R. Acad. Sci. Paris 187 (1928) 870-872. | JFM

[4] W. Feller, On a general class of “contagious” distributions. Ann. Math. Statist. 14 (1943) 389-400. | Zbl

[5] B. Friedman, A simple urn model. Comm. Pure Appl. Math. 2 (1949) 59-70. | MR | Zbl

[6] A. Hald, The compound hypergeometric distribution and a system of single sampling inspection plans based on prior distributions and costs. Technometrics 2 (1960) 275-340. | MR | Zbl

[7] K.G. Janardan, On Characterizing the Markov-Pólya distribution. Sankhyā Ser. A 46 (1984) 444-453. | Zbl

[8] K.G. Janardan and D.J. Schaeffer, A generalization of Markov-Pólya distribution its extensions and applications. Biometrical J. 19 (1977) 87-106. | Zbl

[9] N.L. Johnson and S. Kotz, Urn Models and Their Application. Wiley, New York (1977). | MR | Zbl

[10] C. Jordan, Sur un cas généralisé de la probabilité des épreuves répétées. C. R. Acad. Sci. Paris 184 (1927) 315-317. | JFM

[11] J. Ollero and H.M. Ramos, Description of a Subfamily of the Discrete Pearson System as Generalized-Binomial Distributions. J. Italian Statist. Soc. 2 (1995) 235-249.

[12] J.K. Ord, On a System of Discrete Distributions. Biometrika 54 (1967) 649-656. | MR | Zbl

[13] J.K. Ord, Families of Frequency Distributions. Griffin, London (1972). | MR | Zbl

[14] J. Panaretos and E. Xekalaki, On some distributions arising from certain generalized sampling schemes. Commun. Statist. Theory Meth. 15 (1986) 873-891. | MR | Zbl

[15] J. Panaretos and E. Xekalaki, A probability distribution associated with events with multiple occurrences. Statist. Probab. Lett. 8 (1989) 389-396. | MR | Zbl

[16] G.P. Patil and S.W. Joshi, A Dictionary and Bibliography of Discrete Distributions. Oliver & Boyd, Edinburgh (1968). | MR | Zbl

[17] A.N. Philippou, G.A. Tripsiannis and D.L. Antzoulakos, New Pólya and inverse Pólya distributions of order k. Commun. Statist. Theory Meth. 18 (1989) 2125-2137. | MR | Zbl

[18] G. Pólya, Sur quelques points de la théorie des probabilités. Ann. Inst. H. Poincaré 1 (1930) 117-161. | JFM | Numdam | MR

[19] M. Skibinsky, A characterization of hypergeometric distributions. J. Amer. Statist. Assoc. 65 (1970) 926-929. | MR | Zbl

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