Comptes Rendus
no. 2
Statistics/Probability Theory
Sums, differences, products, and ratios of hypergeometric beta variables
[Sommes, différences, produits et rapports de variables hypergéométriques beta]

Présenté par : Paul Deheuvels

Saralees Nadarajah1
1 Department of Statistics, University of Nebraska, Lincoln, NE 68583, USA
Comptes Rendus. Mathématique, Volume 341 (2005) no. 2, pp. 129-132.

Dans des publications récentes, le Professeur T. Pham-Gia a calculé les distributions de sommes, différences, produits et rapports de variables aléatoires beta indépendantes. Dans cette Note, nous étendons les résultats du Professeur Pham-Gia au cas où X1 and X2 sont des variables aléatoires indépendantes obéissant aux distributions hypergéométriques confluente et de Gauss (qui sont des généralisations de la distribution beta). Pour chacune de ces distributions, nous dérivons des expressions excates des densités S=X1+X2, D=X1−X2, P=X1X2 et R=X2/X1. Ces expressions impliquent des fonctions hypergéométriques de une et deux variables.

Recent papers by Professor T. Pham-Gia derived distributions of sums, differences, products and ratios of independent beta random variables. In this Note we extend Professor Pham-Gia's results when X1 and X2 are independent random variables distributed according to the confluent and Gauss hypergeometric distributions (which are generalizations of the beta distribution). For each of these distributions, we derive exact expressions for the densities of S=X1+X2, D=X1−X2, P=X1X2, and R=X2/X1. The expressions turn out to involve the hypergeometric functions of one and two variables.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2005.06.013
Saralees Nadarajah 1

1 Department of Statistics, University of Nebraska, Lincoln, NE 68583, USA 
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Saralees Nadarajah. Sums, differences, products, and ratios of hypergeometric beta variables. Comptes Rendus. Mathématique, Volume 341 (2005) no. 2, pp. 129-132. doi : 10.1016/j.crma.2005.06.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.06.013/

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