Displaying similar documents to “Comparing the distributions of sums of independent random vectors”

On the rate of approximation in the random sum CLT for dependent variables

Adhir Kumar Basu (1987)

Aplikace matematiky

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Capital " O " and lower-case " o " approximations of the expected value of a class of smooth functions ( f ∈ C r ( R ) ) of the normalized random partial sums of dependent random variables by the expectation of the corresponding functions of Gaussian random variables are established. The same types of approximation are also obtained for dependent random vectors. This generalizes and improves previous results of the author (1980) and Rychlik and Szynal (1979).

Stability estimates of generalized geometric sums and their applications

Evgueni I. Gordienko (2004)

Kybernetika

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The upper bounds of the uniform distance ρ ∑ k = 1 ν X k , ∑ k = 1 ν X ˜ k between two sums of a random number ν of independent random variables are given. The application of these bounds is illustrated by stability (continuity) estimating in models in queueing and risk theory.

On some limit distributions for geometric random sums

Marek T. Malinowski (2008)

Discussiones Mathematicae Probability and Statistics

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We define and give the various characterizations of a new subclass of geometrically infinitely divisible random variables. This subclass, called geometrically semistable, is given as the set of all these random variables which are the limits in distribution of geometric, weighted and shifted random sums. Introduced class is the extension of, considered until now, classes of geometrically stable [5] and geometrically strictly semistable random variables [10]. All the results can be straightforward...

Stochastic ordering of random kth record values

Wiesław Dziubdziela, Agata Tomicka-Stisz (1999)

Applicationes Mathematicae

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Let X 1 , X 2 , . . . be a sequence of independent and identically distributed random variables with continuous distribution function F(x). Denote by X(1,k),X(2,k),... the kth record values corresponding to X 1 , X 2 , . . . We obtain some stochastic comparison results involving the random kth record values X(N,k), where N is a positive integer-valued random variable which is independent of the X i .

Sums of a Random Number of Random Variables and their Approximations with ν- Accompanying Infinitely Divisible Laws

Klebanov, Lev, Rachev, Svetlozar (1996)

Serdica Mathematical Journal

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* Research supported by NATO GRANT CRG 900 798 and by Humboldt Award for U.S. Scientists. In this paper a general theory of a random number of random variables is constructed. A description of all random variables ν admitting an analog of the Gaussian distribution under ν-summation, that is, the summation of a random number ν of random terms, is given. The v-infinitely divisible distributions are described for these ν-summations and finite estimates of the approximation of ν-sum...