Library for FT alpha-Stable ch.f. (fwd)

Library for FT alpha-Stable ch.f. (fwd)

[James Theiler]

Hi Jean,
  thank you for your inquiry; i did not write the Levy code in GSL, 
but i am forwarding your email to the GSL discussion list in case
others have opinions or suggestions.

regards,
jt

-- 
James Theiler
MS-B244, ISR-2, LANL; Los Alamos, NM 87544
Space and Remote Sensing Sciences; Los Alamos National Laboratory
http://public.lanl.gov/jt

---------- Forwarded message ----------
Date: Wed, 2 Jul 2008 02:51:44 -0700 (PDT)
From: Jean Hu <jhu_80@yahoo.com>
To: jt@lanl.gov
Subject: Library for FT alpha-Stable ch.f.

Dear JT:

I reading thru the source code for the Levy library written for GNU.  The statistical model that we are studying is like alpha-stable as only the ch.f. is in closed form.  It will be presented this autumn in Melbourne, AU.  

Have you already considered using Fast Fourier transform for the Fourier transform integral?  
p(x) dx = (1/(2 pi)) \int dt exp(- it x - |c t|^alpha)
If so, was the Frequency Sampling Technique applied in FFT/IFFT adaptive to the alpha parameter for faster computation?  Or was there a bound placed on alpha to imply out Nyquist frequency for your IFFT/FFT?  I look forward to your input.  Thank you for your time and consideration.

Best regards,
J.Hu


      

Re: Library for FT alpha-Stable ch.f. (fwd)

[Brian Gough]

At Wed, 2 Jul 2008 11:55:32 -0600 (MDT),
James Theiler wrote:
> I reading thru the source code for the Levy library written for GNU.  The statistical model that we are studying is like alpha-stable as only the ch.f. is in closed form.  It will be presented this autumn in Melbourne, AU.  
> 
> Have you already considered using Fast Fourier transform for the Fourier transform integral?  
> p(x) dx = (1/(2 pi)) \int dt exp(- it x - |c t|^alpha)
> If so, was the Frequency Sampling Technique applied in FFT/IFFT adaptive to the alpha parameter for faster computation?  Or was there a bound placed on alpha to imply out Nyquist frequency for your IFFT/FFT?  I look forward to your input.  Thank you for your time and consideration.

The FFT method was too complicated for our needs as a general purpose
library so I did not look at it.  We only provide cumulative
distribution functions when they are available in closed form.

-- 
Brian Gough