Re: Normal distribtion
- To: mathgroup at smc.vnet.net
- Subject: [mg49204] Re: Normal distribtion
- From: koopman at sfu.ca (Ray Koopman)
- Date: Wed, 7 Jul 2004 01:42:48 -0400 (EDT)
- References: <7228735a.0407050100.4695fc68@posting.google.com> <QaednZQbSYcwpnTdRVn-vA@comcast.com> <ccdlms$sd5$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
"Roger L. Bagula" <rlbtftn at netscape.net> wrote in message news:<ccdlms$sd5$1 at smc.vnet.net>...
> I found a better faster way to get a Gaussian/ white noise:
> In Mathematica notebook style:
>
> x[a_]=(1+Sqrt[1-a^2))/a
> Noise=Table[Exp[-x[Sin[2*Pi*Random[]]]^2/2/Sqrt[2*Pi],{n,1,500}]
> ListPlot[noise,PlotRange--> All,PlotJoined->True]
>
> It is a projective line ( circle to line random taken as the basic for a
> normal distribution's amplitude.) based algorithm.
> [...]
(1+Sqrt[1-a^2])/a = Cot[ArcSin[a]/2], so
y = x[Sin[2*Pi*Random[]]] = Cot[Pi*Random[]] has a Cauchy distribution.
Exp[-y^2/2]/Sqrt[2*Pi] is the standard normal density function,
but why do you use it here?