Displaying similar documents to “Metrics for multivariate stable distributions”

Estimation of parameters of a spherical invariant stable distribution

Piotr Szymański (2012)

Applicationes Mathematicae

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This paper concerns the estimation of the parameters that describe spherical invariant stable distributions: the index α ∈ (0,2] and the scale parameter σ >0. We present a kind of moment estimators derived from specially transformed original data.

Limit distributions for sums of shrunken random variables

Zbigniew J. Jurek

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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..............................................

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

Grażyna Mazurkiewicz (2010)

Banach Center Publications

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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).

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

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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...

On SαS density function

Grażyna Mazurkiewicz (2005)

Discussiones Mathematicae Probability and Statistics

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In this paper, we study some analytical properties of the symmetric α-stable density function.