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Displaying similar documents to “Limit distributions for sums of shrunken 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).

Drought models based on Burr XII variables

Saralees Nadarajah, B. M. Golam Kibria (2006)

Applicationes Mathematicae

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Burr distributions are some of the most versatile distributions in statistics. In this paper, a drought application is described by deriving the exact distributions of U = XY and W = X/(X+Y) when X and Y are independent Burr XII random variables. Drought data from the State of Nebraska are used.