# Geometrically strictly semistable laws as the limit laws

Discussiones Mathematicae Probability and Statistics (2007)

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

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topMarek 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 -

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