Random continued fractions with beta-hypergeometric distribution

• Autores: Gérard Letac, Mauro Piccioni
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 40, Nº. 3, 2012, págs. 1105-1134
• Idioma: inglés
• DOI: 10.1214/10-AOP642
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• Resumen

  • In a recent paper [Statist. Probab. Lett. 78 (2008) 1711–1721] it has been shown that certain random continued fractions have a density which is a product of a beta density and a hypergeometric function 2F1. In the present paper we fully exploit a formula due to Thomae [J. Reine Angew. Math. 87 (1879) 26–73] in order to generalize substantially the class of random continuous fractions with a density of the above form. This involves the design of seven particular graphs. Infinite paths on them lead to random continued fractions with an explicit distribution. A careful study about the set of five real parameters leading to a beta-hypergeometric distribution is required, relying on almost forgotten results mainly due to Felix Klein.