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MathGroup Archive 1998

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Re: Levy Distribution

  • To: mathgroup at
  • Subject: [mg14827] Re: Levy Distribution
  • From: jenningsj at (Jim Jennings)
  • Date: Wed, 18 Nov 1998 01:29:31 -0500
  • Organization: University of Texas at Austin
  • References: <72je3s$>
  • Sender: owner-wri-mathgroup at

In article <72je3s$3f2 at>, "Yves Gauvreau"
<gauy at> wrote:

>Does someone know this distribution ?  What is the function ?

The Levey-stable distribution cannot be expresed in closed form except
for special cases.  The characteristic function is:

p(v) = exp(i v d - |c v|^a)

a is the Levy index 0<a<=2
c is the width parameter (like variance, except when a<2 variance is
infinite) d is the location parameter

See, for example:

Painter, S, 1995, Random fractal models of heterogeneity: the
Levey-stable approach, Mathematical Geology, v 27, n 7, p 813-830.

Mantegna, R, N, 1994, Fast, accurate algorithm for the numerical
simulation of Levey stable stochastic processes, Physical Review E, v
49, n 5, p 4677-4683.

I know Scott uses Mathematica, if you can locate him he might have some
useful stuff to share.

Jim Jennings                                 Research Associate         
jenningsj at Bureau of Economic Geology      (512)
471-4364 (voice) University of Texas at Austin   (512) 471-0140 (fax)

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