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A method constructing density functions: the case of a generalized Rayleigh variable

Viorel Gh. Vodă (2009)

Applications of Mathematics

In this paper we propose a new generalized Rayleigh distribution different from that introduced in Apl. Mat. 47 (1976), pp. 395–412. The construction makes use of the so-called “conservability approach” (see Kybernetika 25 (1989), pp. 209–215) namely, if X is a positive continuous random variable with a finite mean-value E ( X ) , then a new density is set to be f 1 ( x ) = x f ( x ) / E ( X ) , where f ( x ) is the probability density function of X . The new generalized Rayleigh variable is obtained using a generalized form of the exponential...

A note on Pólya's theorem.

Dinis Pestana (1984)

Trabajos de Estadística e Investigación Operativa

The class of extended Pólya functions Ω = {φ: φ is a continuous real valued real function, φ(-t) = φ(t) ≤ φ(0) ∈ [0,1], límt→∞ φ(t) = c ∈ [0,1] and φ(|t|) is convex} is a convex set. Its extreme points are identified, and using Choquet's theorem it is shown that φ ∈ Ω has an integral representation of the form φ(|t|) = ∫0∞ max{0, 1-|t|y} dG(y), where G is the distribution function of some random variable Y. As on the other hand max{0, 1-|t|y} is the characteristic function of an absolutely continuous...

A simple proof of Fishburn's moments theorem.

María Lina Martínez García (1985)

Trabajos de Estadística e Investigación Operativa

We derive a necessary condition for stochastic dominance of any order based on the Laplace transform of probability measures on [0,∞) for which it follows easily Fishburn's theorem on the lexicographic order of the moments.

About the density of spectral measure of the two-dimensional SaS random vector

Marta Borowiecka-Olszewska, Jolanta K. Misiewicz (2003)

Discussiones Mathematicae Probability and Statistics

In this paper, we consider a symmetric α-stable p-sub-stable two-dimensional random vector. Our purpose is to show when the function e x p - ( | a | p + | b | p ) α / p is a characteristic function of such a vector for some p and α. The solution of this problem we can find in [3], in the language of isometric embeddings of Banach spaces. Our proof is based on simple properties of stable distributions and some characterization given in [4].

About the generating function of a left bounded integer-valued random variable

Charles Delorme, Jean-Marc Rinkel (2008)

Bulletin de la Société Mathématique de France

We give a relation between the sign of the mean of an integer-valued, left bounded, random variable X and the number of zeros of 1 - Φ ( z ) inside the unit disk, where Φ is the generating function of X , under some mild conditions

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