Displaying similar documents to “Comparisons between tail probabilities of sums of independent symmetric random variables”

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...

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 .