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May 2012 Random continued fractions with beta-hypergeometric distribution
Gérard Letac, Mauro Piccioni
Ann. Probab. 40(3): 1105-1134 (May 2012). DOI: 10.1214/10-AOP642

Abstract

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.

Citation

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Gérard Letac. Mauro Piccioni. "Random continued fractions with beta-hypergeometric distribution." Ann. Probab. 40 (3) 1105 - 1134, May 2012. https://doi.org/10.1214/10-AOP642

Information

Published: May 2012
First available in Project Euclid: 4 May 2012

zbMATH: 1244.60067
MathSciNet: MR2962088
Digital Object Identifier: 10.1214/10-AOP642

Subjects:
Primary: 60J05
Secondary: 60E05

Keywords: Distributions on (0,1) with five parameters , generalized hypergeometric functions , periodic random continued fractions

Rights: Copyright © 2012 Institute of Mathematical Statistics

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Vol.40 • No. 3 • May 2012
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