Displaying similar documents to “A geometrical approach to the special stable distributions”

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

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.

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 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.

Around stable forking

Byunghan Kim, A. Pillay (2001)

Fundamenta Mathematicae

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We discuss various conjectures and problems around the issue of when and whether stable formulas are responsible for forking in simple theories. We prove that if the simple theory T has strong stable forking then any complete type is a nonforking extension of a complete type which is axiomatized by instances of stable formulas. We also give another treatment of the first author's result which identifies canonical bases in supersimple theories.

A Note on the Uniqueness of Stable Marriage Matching

Ewa Drgas-Burchardt (2013)

Discussiones Mathematicae Graph Theory

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In this note we present some sufficient conditions for the uniqueness of a stable matching in the Gale-Shapley marriage classical model of even size. We also state the result on the existence of exactly two stable matchings in the marriage problem of odd size with the same conditions.

Decompositions of saturated models of stable theories

M. C. Laskowski, S. Shelah (2006)

Fundamenta Mathematicae

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We characterize the stable theories T for which the saturated models of T admit decompositions. In particular, we show that countable, shallow, stable theories with NDOP have this property.

Metrics for multivariate stable distributions

John P. Nolan (2010)

Banach Center Publications

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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...

Vector Optimization Results for ℓ -Stable Data

Marie Dvorská (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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The aim of this paper is to summarize basic facts about ℓ -stable at a point vector functions and existing results for certain vector constrained programming problem with ℓ -stable data.