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On SαS density function

100%

Mazurkiewicz G.

Discussiones Mathematicae Probability and Statistics

2005

tom 25

nr 1

91-101

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

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

100%

Mazurkiewicz G.

Banach Center Publications

2010

tom 90

nr 1

79-82

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).

Ograniczanie wyników

1 Banach Center Publications

1 Discussiones Mathematicae Probability and Statistics

2 Mazurkiewicz G.

1 2010

1 2005

Wyniki wyszukiwania

On SαS density function

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