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Geometrically strictly semistable laws as the limit laws

100%

Malinowski M.

Discussiones Mathematicae Probability and Statistics

2007

tom 27

nr 1-2

79-97

A random variable X is geometrically infinitely divisible iff for every p ∈ (0,1) there exists random variable $X_p$ such that $X\stackrel{d}{=} ∑_{k=1}^{T(p)}X_{p,k}$, where $X_{p,k}$'s are i.i.d. copies of $X_p$, and random variable T(p) independent of ${X_{p,1},X_{p,2},...}$ has geometric distribution with the parameter p. In the paper we give some new characterization of geometrically infinitely divisible distribution. The main results concern geometrically strictly semistable distributions which form a subset of geometrically infinitely divisible distributions. We show that they are limit laws for random and deterministic sums of independent random variables.

Stochastic ordering of random kth record values

100%

Dziubdziela W., Tomicka-Stisz A.

Applicationes Mathematicae

1999

tom 26

nr 3

293-298

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 $X_i$.

Ograniczanie wyników

1 Applicationes Mathematicae

1 Discussiones Mathematicae Probability and Statistics

1 Dziubdziela W.

1 Malinowski M.

1 Tomicka-Stisz A.

1 2007

1 1999

Wyniki wyszukiwania

Geometrically strictly semistable laws as the limit laws

Stochastic ordering of random kth record values