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Displaying similar documents to “A note on stability of multivariate distributions.”

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).

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

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...

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

José María Sarabia, Emilio Gómez-Déniz (2008)

SORT

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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...

Discrete generalized Liouville-type distribution and related multivariate distributions.

G. S. Lingappaiah (1984)

Trabajos de Estadística e Investigación Operativa

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Discrete analogue of the Liouville distribution is defined and is termed as Discrete Generalized Liouville-Type Distribution (DGL-TD). Firstly, properties in its factorial and ordinary moments are given. Then by finding the covariance matrix, partial and multiple correlations for DGL-TD are evaluated. Multinomial, multivariate negative binomial and multivariate log series distributions are shown as particular cases of this general distribution. The asymptotic distribution of the estimates...

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.

Geometric Stable Laws Through Series Representations

Kozubowski, Tomasz, Podgórski, Krzysztof (1999)

Serdica Mathematical Journal

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Let (Xi ) be a sequence of i.i.d. random variables, and let N be a geometric random variable independent of (Xi ). Geometric stable distributions are weak limits of (normalized) geometric compounds, SN = X1 + · · · + XN , when the mean of N converges to infinity. By an appropriate representation of the individual summands in SN we obtain series representation of the limiting geometric stable distribution. In addition, we study...