HCM property and the half-Cauchy distribution

  1. Pierre Bosch

Abstract

Let Zα and ~Zβ be two independent positive -stable random variables. It is known that (Z α/~Zα )α is distributed as the positive branch of a Cauchy random variable with drift. We show that the density of the power transformation (Zα /~Z α) β 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.

Download article

This article

Probability and Mathematical Statistics

35, z. 2, 2015

Pages from 191 to 200

Other articles by author

Google Scholar

zamknij

Your cart (products: 0)

No products in cart

Your cart Checkout