Re: Re: Normal distribtion

*To*: mathgroup at smc.vnet.net*Subject*: [mg49233] Re: [mg49201] Re: Normal distribtion*From*: DrBob <drbob at bigfoot.com>*Date*: Thu, 8 Jul 2004 02:51:12 -0400 (EDT)*References*: <7228735a.0407050100.4695fc68@posting.google.com> <QaednZQbSYcwpnTdRVn-vA@comcast.com> <ccdlms$sd5$1@smc.vnet.net> <200407070542.BAA25013@smc.vnet.net> <opsar4ygzgiz9bcq@monster.cox-internet.com> <40EC4EF3.4010802@netscape.net> <opsasec0j9iz9bcq@monster.cox-internet.com> <40EC7792.3070705@netscape.net>*Sender*: owner-wri-mathgroup at wolfram.com

I don't get error messages from the notebook, which just proves it isn't the same code. In the post I responded to, you had: x[a_] = (1 + Sqrt[a])/a In the notebook, you have: x[a_] = (1 + Sqrt[1 - a^2])/a So... Does that really make me a complainer? Bobby On Wed, 07 Jul 2004 15:22:10 -0700, Roger L. Bagula <rlbtftn at netscape.net> wrote: > Dear Dr. Bob, > So far you are the only complainer about it not working. > I'm using Mathematica 3.01. > I'm sending a notbook with this. > 5.01 should translate it. > I can only get you a version 4.01 with my classic Mac os 9.2 > and I have to use another start up disk to do that because the reader > nullifies my 3.01 > if I use the same disk partition. > DrBob wrote: > >> That code doesn't work in Mathematica 5.0.1. What software do you mean >> by "3d"? >> >> Bobby >> >> On Wed, 07 Jul 2004 12:28:51 -0700, Roger L. Bagula >> <rlbtftn at netscape.net> wrote: >> >>> Dear DrBob, >>> I just did it in 3d. >>> It works so fine! >>> DrBob wrote: >>> >>>> Did you test that code? >>>> >>>> Sin is often negative, hence x[Sin[....]] is Complex. Listplot, Max, >>>> Min, and Floor can't handle complex data, so there are LOTS of error >>>> messages. >>>> >>>> Bobby >>>> >>>> On Wed, 7 Jul 2004 01:42:40 -0400 (EDT), Roger L. Bagula >>>> <rlbtftn at netscape.net> wrote: >>>> >>>>> To give a way of showing the symmetrical distribution >>>>> I worked this program up. >>>>> I use the Sign[2*Random[]-1] trick to get an equal sign distribution >>>>> so that both sides of the distribution which is even can be seen. >>>>> Since this distribution is closer to single valued on the real line >>>>> even a 10000 it is very noisy. >>>>> An equalized distribution with count: >>>>> x[a_]=(1+Sqrt[a])/a >>>>> noise=Table[Sign[2*Random[]-1]*Exp[-x[Sin[2*Pi*(2*Random[]-1)]]^2/2]/Sqrt[2*Pi],{n,1, >>>>> 10000}]; >>>>> ListPlot[noise,PlotRange->All, PlotJoined-> True] >>>>> b=Table[Floor[2500*noise[[n]]],{n,1,10000}]; >>>>> b0=Dimensions[b][[1]] >>>>> bmax=Max[b] >>>>> bmin=Min[b] >>>>> c=Table[Count[b,n],{n,Floor[bmin],bmax}]; >>>>> ListPlot[c,PlotJoined->True,PlotRange->All] >>>>> 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>

**Re: sorting polynomials by the degree of certain terms**

**monte carlo simulations**

**Re: Re: Normal distribtion**

**Re: Normal distribtion**