Displaying similar documents to “Sums of a Random Number of Random Variables and their Approximations with ν- Accompanying Infinitely Divisible Laws”

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 .

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...