# Geometrically strictly semistable laws as the limit laws

• Volume: 27, Issue: 1-2, page 79-97
• ISSN: 1509-9423

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## Abstract

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A random variable X is geometrically infinitely divisible iff for every p ∈ (0,1) there exists random variable ${X}_{p}$ such that $X\stackrel{d}{=}{\sum }_{k=1}^{T\left(p\right)}{X}_{p,k}$, 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.

## How to cite

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Marek T. Malinowski. "Geometrically strictly semistable laws as the limit laws." Discussiones Mathematicae Probability and Statistics 27.1-2 (2007): 79-97. <http://eudml.org/doc/277030>.

@article{MarekT2007,
abstract = {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.},
author = {Marek T. Malinowski},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {infinite divisibility; geometric infinite divisibility; geometric semistability; random sums; limit laws; characteristic function},
language = {eng},
number = {1-2},
pages = {79-97},
title = {Geometrically strictly semistable laws as the limit laws},
url = {http://eudml.org/doc/277030},
volume = {27},
year = {2007},
}

TY - JOUR
AU - Marek T. Malinowski
TI - Geometrically strictly semistable laws as the limit laws
JO - Discussiones Mathematicae Probability and Statistics
PY - 2007
VL - 27
IS - 1-2
SP - 79
EP - 97
AB - 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.
LA - eng
KW - infinite divisibility; geometric infinite divisibility; geometric semistability; random sums; limit laws; characteristic function
UR - http://eudml.org/doc/277030
ER -

## References

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8. [8] N.R. Mohan, R. Vasudeva and H.V. Hebbar, On geometrically infinitely divisible laws and geometric domains of attraction, Sankhya Ser. A 55 (1993), 171-179. Zbl0803.60017
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