UNIVERSITY
OF WROCŁAW
 
Main Page
Contents
Online First
General Information
Instructions for authors


VOLUMES
43.2 43.1 42.2 42.1 41.2 41.1 40.2
40.1 39.2 39.1 38.2 38.1 37.2 37.1
36.2 36.1 35.2 35.1 34.2 34.1 33.2
33.1 32.2 32.1 31.2 31.1 30.2 30.1
29.2 29.1 28.2 28.1 27.2 27.1 26.2
26.1 25.2 25.1 24.2 24.1 23.2 23.1
22.2 22.1 21.2 21.1 20.2 20.1 19.2
19.1 18.2 18.1 17.2 17.1 16.2 16.1
15 14.2 14.1 13.2 13.1 12.2 12.1
11.2 11.1 10.2 10.1 9.2 9.1 8
7.2 7.1 6.2 6.1 5.2 5.1 4.2
4.1 3.2 3.1 2.2 2.1 1.2 1.1
 
 
WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 35, Fasc. 2,
pages 191 - 200
 

HCM PROPERTY AND THE HALF-CAUCHY DISTRIBUTION

Pierre Bosch

Abstract: Let Z α and ˜Z α be two independent positive α -stable random variables. It is known that (Z ∕˜Z )α α α is distributed as the positive branch of a Cauchy random variable with drift. We show that the density of the power transformation (Z ∕˜Z )β α α is hyperbolically completely monotone in the sense of Thorin and Bondesson if and only if α ≤ 1∕2 and |β| ≥ α∕(1- α). This clarifies a conjecture of Bondesson (1992) on positive stable densities.

2000 AMS Mathematics Subject Classification: Primary: 60E07; Secondary: 60E05.

Keywords and phrases: Half-Cauchy distribution, complete monotonicity, generalized gamma convolution, hyperbolically completely monotone function, Pick function, positive stable density.

Download:    Abstract    Full text   Abstract + References