# On some limit distributions for geometric random sums

Discussiones Mathematicae Probability and Statistics (2008)

- Volume: 28, Issue: 2, page 247-266
- ISSN: 1509-9423

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topMarek T. Malinowski. "On some limit distributions for geometric random sums." Discussiones Mathematicae Probability and Statistics 28.2 (2008): 247-266. <http://eudml.org/doc/277016>.

@article{MarekT2008,

abstract = {We define and give the various characterizations of a new subclass of geometrically infinitely divisible random variables. This subclass, called geometrically semistable, is given as the set of all these random variables which are the limits in distribution of geometric, weighted and shifted random sums. Introduced class is the extension of, considered until now, classes of geometrically stable [5] and geometrically strictly semistable random variables [10]. All the results can be straightforward transfered to the case of random vectors in $ℝ^d$.},

author = {Marek T. Malinowski},

journal = {Discussiones Mathematicae Probability and Statistics},

keywords = {random sum; infinite divisibility; semistability; geometric infinite divisibility; geometric stability; geometric semistability; characteristic function; limit distribution; Lévy process},

language = {eng},

number = {2},

pages = {247-266},

title = {On some limit distributions for geometric random sums},

url = {http://eudml.org/doc/277016},

volume = {28},

year = {2008},

}

TY - JOUR

AU - Marek T. Malinowski

TI - On some limit distributions for geometric random sums

JO - Discussiones Mathematicae Probability and Statistics

PY - 2008

VL - 28

IS - 2

SP - 247

EP - 266

AB - We define and give the various characterizations of a new subclass of geometrically infinitely divisible random variables. This subclass, called geometrically semistable, is given as the set of all these random variables which are the limits in distribution of geometric, weighted and shifted random sums. Introduced class is the extension of, considered until now, classes of geometrically stable [5] and geometrically strictly semistable random variables [10]. All the results can be straightforward transfered to the case of random vectors in $ℝ^d$.

LA - eng

KW - random sum; infinite divisibility; semistability; geometric infinite divisibility; geometric stability; geometric semistability; characteristic function; limit distribution; Lévy process

UR - http://eudml.org/doc/277016

ER -

## References

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