R help - Sep 2008 - fft: from characteristic funtion to density function

Hello all!
I've posted the question before but I am still struggling for an
answer, please help if you can;-)

Suppose a discrete series of data is generated by the following
equation:
CF=exp(-(t^2)/2)
which is the characteristic function of a random variable X with
standard normal distribution, how do I *numerically* solve for its
probability density function? i.e., obtain a series of data that plots
a well know bell-shape curve? Or, find x such that Pr(X<x)=0.05?

I have no problem to derive the forward and inverse Fourier equation
pair, but just no clue on numerical method. A working code on this
simplest exercise
would clear off many, many of my confusions
I have generated CF with t of 256 points equally spaced between -4 to
4 in Excel, but don't know
how to proceed.

Thanks for your help!
Jindan

take a look at
http://finzi.psych.upenn.edu/R/Rhelp02a/archive/130153.html

hth,
Matthias


Jindan Zhou wrote:
> Hello all!
> I've posted the question before but I am still struggling for an
> answer, please help if you can;-)
>
> Suppose a discrete series of data is generated by the following
> equation:
> CF=exp(-(t^2)/2)
> which is the characteristic function of a random variable X with
> standard normal distribution, how do I *numerically* solve for its
> probability density function? i.e., obtain a series of data that plots
> a well know bell-shape curve? Or, find x such that Pr(X<x)=0.05?
>
> I have no problem to derive the forward and inverse Fourier equation
> pair, but just no clue on numerical method. A working code on this
> simplest exercise
> would clear off many, many of my confusions
> I have generated CF with t of 256 points equally spaced between -4 to
> 4 in Excel, but don't know
> how to proceed.
>
> Thanks for your help!
> Jindan
>
> ______________________________________________
> R-help at 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.
>   
-- 
Dr. Matthias Kohl
www.stamats.de