Displaying similar documents to “On a conditional Cauchy functional equation of several variables and a characterization of multivariate stable distributions.”

On the infinite divisibility of scale mixtures of symmetric α-stable distributions, α ∈ (0,1]

Grażyna Mazurkiewicz (2010)

Banach Center Publications

Similarity:

The paper contains a new and elementary proof of the fact that if α ∈ (0,1] then every scale mixture of a symmetric α-stable probability measure is infinitely divisible. This property is known to be a consequence of Kelker's result for the Cauchy distribution and some nontrivial properties of completely monotone functions. It is known that this property does not hold for α = 2. The problem discussed in the paper is still open for α ∈ (1,2).

Construction of multivariate distributions: a review of some recent results.

José María Sarabia, Emilio Gómez-Déniz (2008)

SORT

Similarity:

The construction of multivariate distributions is an active field of research in theoretical and applied statistics. In this paper some recent developments in this field are reviewed. Specifically, we study and review the following set of methods: (a) Construction of multivariate distributions based on order statistics, (b) Methods based on mixtures, (c) Conditionally specified distributions, (d) Multivariate skew distributions, (e) Distributions based on the method of the variables...

Limit distributions for sums of shrunken random variables

Zbigniew J. Jurek

Similarity:

CONTENTSIntroduction....................................................................................................................................................................... 5Chapter I. Distributions of sums or infinitesimal random variables § 1. Notations, definitions and preliminary facts.......................................................................................... 6 § 2. Existence of limit distributions for sums of infinitesimal random variables..............................................

Metrics for multivariate stable distributions

John P. Nolan (2010)

Banach Center Publications

Similarity:

Metrics are proposed for the distance between two multivariate stable distributions. The first set of metrics are defined in terms of the closeness of the parameter functions of one dimensional projections of the laws. Convergence in these metrics is equivalent to convergence in distribution and an explicit bound on the uniform closeness of two stable densities is given. Another metric based on the Prokhorov metric between the spectral measures is related to the first metric. Consequences...

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

German Bernhart, Jan-Frederik Mai, Matthias Scherer (2015)

Dependence Modeling

Similarity:

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...