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A direct approach to the stable distributions

Published online by Cambridge University Press:  25 July 2016

Jim Pitman*
Affiliation:
University of California, Berkeley
*
Statistics Department, University of California, Berkeley, 367 Evans Hall, Berkeley, CA94720‒3860, USA. Email address: pitman@stat.berkeley.edu

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.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 2016 

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