Title :

Convolution of beta prime distribution

Author(s) :

Ferreira, Rui [Auteur]
Simon, Thomas [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Transactions of the American Mathematical Society

Pages :

855-890

Publisher :

American Mathematical Society

Publication date :

2023-01-02

ISSN :

0002-9947

English keyword(s) :

Appell series
Beta prime distribution
Complete monotonicity
Confluent hypergeometric function
Hypergeometric series
Mill’s ratio
Parabolic cylinder function
Self-decomposability
Stochastic ordering
Thomae’s relations
Thorin measure
Turán’s inequality.

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

We establish some identities in law for the convolution of a beta prime distribution with itself, involving the square root of beta distributions. The proof of these identities relies on transformations on generalized ...
Show more >We establish some identities in law for the convolution of a beta prime distribution with itself, involving the square root of beta distributions. The proof of these identities relies on transformations on generalized hypergeometric series obtained via Appell series of the first kind and Thomae’s relationships for ${}_3F_2(1).$ Using a self-decomposability argument, the identities are applied to derive complete monotonicity properties for quotients of confluent hypergeometric functions having a doubling character. By means of probability, we also obtain a simple proof of Turán’s inequality for the parabolic cylinder function and the confluent hypergeometric function of the second kind. The case of Mill’s ratio is discussed in detail.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL