Re: density of the ratio of levy variables [corrected]

In article <1185263004.500383.130800@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
<george.klimmt@xxxxxxxxx> wrote:
I correct my previous post: I'm looking for the density of a ratio of
two independent TWO-PARAMETER (location and dispersion) levy
distributed variables (not unshifted levy).

Thanks a lot,

George.

If X and Y are random variables with a Fourier transform
E(exp(iuX + ivY)) = h(u, v), the cdf of X/Y at z, if Y > 0,
is given by

F_Z(z) = 1/2 - 1/(2*pi*i)*\int(h(u-zu)/u) du,

where the integral is the Cauchy principal value at 0.
Assuming regularity conditions are satisfied, the density
is given by the derivative of this, with differentiation
under the integral sign permitted.

If Y is not positive, the problem is harder.



--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.

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