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?