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A direct approach to the stable distributions

Part of: Distribution theory - Probability

Published online by Cambridge University Press:  25 July 2016

E. J. G. Pitman  and
Jim Pitman
Jim Pitman*
Affiliation:
University of California, Berkeley
*
Statistics Department, University of California, Berkeley, 367 Evans Hall, Berkeley, CA94720‒3860, USA. Email address: [email protected]
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Abstract

The explicit form for the characteristic function of a stable distribution on the line is derived analytically by solving the associated functional equation and applying the theory of regular variation, without appeal to the general Lévy‒Khintchine integral representation of infinitely divisible distributions.

Keywords

Stable distributioncharacteristic functionregular variationinfinitely divisible distributionLévy‒Khintchine formulaEulerian integral

MSC classification

Primary: 60E07: Infinitely divisible distributions; stable distributions
Type
Research Article
Information
Advances in Applied Probability , Volume 48 , Issue A: Probability, Analysis and Number Theory , July 2016 , pp. 261 - 282
Copyright
Copyright © Applied Probability Trust 2016 

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