Univariate Geometric Stable Laws

T. J. Kozubowski; S. T. Rachev

doi:10.1023/A:1022629726024

Univariate Geometric Stable Laws

T. J. Kozubowski, S. T. Rachev

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

60 Scopus citations

Abstract

The paper summarizes recent advances in the theory of geometric stable (GS) distributions. The results presented include parametrizations, characterizations, mixture representations, properties, asymptotic and convergent series expansions of densities and distribution functions, moments and tail behavior, simulation, and estimation.

Original language	English
Pages (from-to)	177-217
Number of pages	41
Journal	Journal of Computational Analysis and Applications
Volume	1
Issue number	2
DOIs	https://doi.org/10.1023/A:1022629726024
State	Published - 1999

Keywords

Geometric compound
Heavy-tail modeling
Linnik distribution
Mittag-Leffler law
Random summation

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10.1023/A:1022629726024

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title = "Univariate Geometric Stable Laws",

abstract = "The paper summarizes recent advances in the theory of geometric stable (GS) distributions. The results presented include parametrizations, characterizations, mixture representations, properties, asymptotic and convergent series expansions of densities and distribution functions, moments and tail behavior, simulation, and estimation.",

keywords = "Geometric compound, Heavy-tail modeling, Linnik distribution, Mittag-Leffler law, Random summation",

author = "Kozubowski, {T. J.} and Rachev, {S. T.}",

note = "Funding Information: Kozubowski's research was partially supported by a Faculty Research Grant from UTC. The research of S. T. Rachev was partially supported by the Deutsche Forschungsgemeinschaft and a grant from the University of California at Santa Barbara.",

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N1 - Funding Information: Kozubowski's research was partially supported by a Faculty Research Grant from UTC. The research of S. T. Rachev was partially supported by the Deutsche Forschungsgemeinschaft and a grant from the University of California at Santa Barbara.

PY - 1999

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KW - Geometric compound

KW - Heavy-tail modeling

KW - Linnik distribution

KW - Mittag-Leffler law

KW - Random summation

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M3 - Article

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SP - 177

EP - 217

JO - Journal of Computational Analysis and Applications

JF - Journal of Computational Analysis and Applications

IS - 2

ER -

Univariate Geometric Stable Laws

Abstract

Keywords

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