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A characterization of probability measures by f-moments

100%

Urbanik K.

Studia Mathematica

1996

tom 118

nr 2

185-204

Given a real-valued continuous function ƒ on the half-line [0,∞) we denote by P*(ƒ) the set of all probability measures μ on [0,∞) with finite ƒ-moments $ʃ_{0}^{∞} ƒ(x)μ^{*n}(dx)$ (n = 1,2...). A function ƒ is said to have the identification property} if probability measures from P*(ƒ) are uniquely determined by their ƒ-moments. A function ƒ is said to be a Bernstein function} if it is infinitely differentiable on the open half-line (0,∞) and $(-1)^{n} ƒ^{(n+1)}(x)$ is completely monotone for some nonnegative integer n. The purpose of this paper is to give a necessary and sufficient condition in terms of the representing measures for Bernstein functions to have the identification property.

On the construction of low-parametric families of min-stable multivariate exponential distributions in large dimensions

88%

Bernhart G., Mai J.-F., Scherer M.

Dependence Modeling

2015

tom 3

nr 1

Min-stable multivariate exponential (MSMVE) distributions constitute an important family of distributions, among others due to their relation to extreme-value distributions. Being true multivariate exponential models, they also represent a natural choicewhen modeling default times in credit portfolios. Despite being well-studied on an abstract level, the number of known parametric families is small. Furthermore, for most families only implicit stochastic representations are known. The present paper develops new parametric families of MSMVE distributions in arbitrary dimensions. Furthermore, a convenient stochastic representation is stated for such models, which is helpful with regard to sampling strategies.

Ograniczanie wyników

1 Dependence Modeling

1 Studia Mathematica

1 Bernhart G.

1 Mai J.-F.

1 Scherer M.

1 Urbanik K.

1 2015

1 1996

Wyniki wyszukiwania

A characterization of probability measures by f-moments

On the construction of low-parametric families of min-stable multivariate exponential distributions in large dimensions