[prev in list] [next in list] [prev in thread] [next in thread] 

List:       r-help
Subject:    Re: [R] fft: characteristic function to distribution
From:       Prof Brian Ripley <ripley () stats ! ox ! ac ! uk>
Date:       2008-04-30 14:38:41
Message-ID: alpine.LFD.1.10.0804301535550.14424 () gannet ! stats ! ox ! ac ! uk
[Download RAW message or body]

On Wed, 30 Apr 2008, Thomas Steiner wrote:

> The characteristic function is the inverse Fourier transform of the
> distribution function. The characteristic function of a normaly
> distributed random variable is exp(-t^2/2).

The fft is a discrete Fourier transforn, not a continuous one.
Further in each case where the normalizing constants are placed and the 
units of frequecy differ from source to source.

?fft has references to exactly what it computes: please consult them.

>
> x=seq(-2,2,length=100)
> fft(pnorm(x),inverse=T)/length(x)
> exp(-x^2/2)
>
> Why aren't the inverse fft and the mentioned function the same?
> Thanks for help,
> Thomas
>
> ______________________________________________
> R-help@r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

-- 
Brian D. Ripley,                  ripley@stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

______________________________________________
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
[prev in list] [next in list] [prev in thread] [next in thread]