Re: Re: Normal distribtion

*To*: mathgroup at smc.vnet.net*Subject*: [mg49341] Re: [mg49326] Re: Normal distribtion*From*: DrBob <drbob at bigfoot.com>*Date*: Thu, 15 Jul 2004 07:00:04 -0400 (EDT)*References*: <7228735a.0407050100.4695fc68@posting.google.com> <QaednZQbSYcwpnTdRVn-vA@comcast.com> <ccdlms$sd5$1@smc.vnet.net> <200407141129.HAA26886@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

No, it probably doesn't. It's not a Normal distribution, after all. Bobby On Wed, 14 Jul 2004 07:29:32 -0400 (EDT), Roger L. Bagula <rlbtftn at netscape.net> wrote: > Abrupt peak due to product of Gaussian distributions: > http://mathworld.wolfram.com/NormalProductDistribution.html > Probably doesn't have Kurtosis near zero either. > Roger L. Bagula wrote: >> 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. >> Since it doesn't use either the polar method with has a choice loop or >> the older 12 random method, the random operation has only to be used >> once for each noise value. >> It is faster by several factors and can be translated to almost any >> language. >> George Marsaglia wrote: >> >>> "philou" <philou2000 at msn.com> wrote in message >>> news:7228735a.0407050100.4695fc68 at posting.google.com... >>> >>> >>>> Hi, >>>> I heard that it was possible to get a realisation of a normal >>>> distribution from two realisations of an uniform distribution. Can >>>> someone explain me how to do that ? What transformations should I do ? >>> >>> >>> Your hazy reference may have been based on my polar method for >>> generating a pair of independent standard normal variates X and Y: >>> >>> If U and V are independent uniform in (-1,1), conditioned by >>> >>> S = U^2+V^2 < 1 >>> >>> then S is uniform in (0,1) and independent of the point >>> (U/sqrt(S),V/sqrt(S)), which is uniform on the unit circumference. >>> >>> Thus if R=sqrt(-2*ln(S)/S) then >>> X=R*U >>> Y=R*V >>> are a pair independent standard normal variates, obtained by >>> projecting that uniform point on the unit circumference >>> a random distance with a root-chi-square-2 distribution, >>> exploiting the uniformity of S and its independence of >>> the random point on the circumference. >>> >>> Of course one has to discard uniform (-1,1) pairs U,V >>> for which S=U^2+V^2>1, so each normal variate is produced >>> at an average cost of 4/pi=1.27 uniform variates. >>> >>> This method is sometimes improperly attributed to Box and Muller, >>> who pointed out that pairs of normal variates could be generated as >>> rho*cos(theta), rho*sin(theta) with rho root-chisquare-2 , sqrt(-2*ln(U)), >>> and theta uniform in (0,2pi), a result we owe to Laplace, who showed us >>> how to find the infinite integral of exp(-x^2) by getting its square >>> as the integral of exp(-x^2-y^2), then transforming to polar coordinates. >>> >>> For a method faster than my polar method, requiring about 1.01 uniform >>> variates per normal variate, try the ziggurat method of >>> Marsaglia and Tsang, in volume 5, Journal of Statistical Software: >>> http://www.jstatsoft.org/index.php?vol=5 >>> >>> George Marsaglia >>> >>> >> >> > > -- DrBob at bigfoot.com www.eclecticdreams.net

**References**:**Re: Normal distribtion***From:*"Roger L. Bagula" <rlbtftn@netscape.net>