Title :

On the infinite divisibility of inverse Beta distributions

Author(s) :

Bosch, Pierre [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Simon, Thomas [Auteur]
Laboratoire de Physique Théorique et Modèles Statistiques [LPTMS]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

English keyword(s) :

Beta distribution
Gamma distribution
Generalized Gamma convolution
Hyperbolically complete monotonicity
Hypergeometric series
Lévy perpetuity
Self-decomposability
Stieltjes transform

HAL domain(s) :

Mathématiques [math]/Probabilités [math.PR]

English abstract : [en]

We show that all negative powers B_{a,b}^-{s} of the Beta distribution are infinitely divisible. The case b<1 follows by complete monotonicity, the case b > 1, s > 1 by hyperbolically complete monotonicity and the case b ...
Show more >We show that all negative powers B_{a,b}^-{s} of the Beta distribution are infinitely divisible. The case b<1 follows by complete monotonicity, the case b > 1, s > 1 by hyperbolically complete monotonicity and the case b > 1, s < 1 by a Lévy perpetuity argument involving the hypergeometric series. We also observe that B_{a,b}^{-s} is self-decomposable whenever 2a + b + s + bs > 1, and that it is not always a generalized Gamma convolution. On the other hand, we prove that all negative powers of the Gamma distribution are generalized Gamma convolutions, answering to a recent question of L. Bondesson.Show less >

Language :

Anglais

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Submission date :

2025-01-22T07:14:19Z