Path: utzoo!utgpu!news-server.csri.toronto.edu!mailrus!ncar!mephisto!prism!bb16
From: bb16@prism.gatech.EDU (Scott Bostater)
Newsgroups: comp.sys.ibm.pc.programmer
Subject: Re: Random Number Generation in Turbo C 2.0
Message-ID: <7078@hydra.gatech.EDU>
Date: 15 Mar 90 13:46:29 GMT
References: <21720@netnews.upenn.edu> <4491@jhunix.HCF.JHU.EDU> <1990Mar14.195315.2985@agate.berkeley.edu>
Reply-To: bb16@prism.gatech.EDU (Scott Bostater)
Distribution: usa
Organization: Georgia Institute of Technology
Lines: 46

In article <1990Mar14.195315.2985@agate.berkeley.edu> raymond@math.berkeley.edu (Raymond Chen) writes:
>eisen@jhunix.UUCP (Gunther Wil Anderson) presented an algorithm
>that claims to produce normally-distributed random numbers.
>
>If you read the code carefully, however, you'll observe that
>it really doesn't do that.  It merely produces a crude approximation
>to a normal distribution, based on the principle that the sum
>of a large number of uniform distributions looks sort of like
>a normal distribution.

And a rough approximation at that.  Try summing 10 to 15 points for something
close.
>
>In particular, the function will never return values with absolute
>value greater than sqrt(12).
>
    [ details of doing the intergral to compute normal distribution omited]

There is a quick and easy transformation that takes 2 independant uniform 
variables and provides 2 independant normal (or gaussian) random variables.

Essentially, given:
  a,b        { random variables uniform [0,1] }
  sigma      { standard deviation of gaussian variables }
  mean       { mean of gaussian variables }

Then

   u = 2 * pi * a
   v = Sqrt(2) * Sqrt( -ln(b))          { thats log base e }

   x = Cos( u) * v * sigma + mean
   y = Sin( u) * v * sigma + mean

x & y are now N(mean,sigma) distributed independant vairables.

References:  1) _Probabilty,_Random_Variables,_and_Stochastic_Processes_ by
                 Athanasios Papoulis      (losey text, good reference)
             2) _Numerical_Respicies_in_[C|Pascal|Fortran]_  (unsure of author) 
                (very good references, wish I owned a copy :-)
             3) _EE_6051_Homework__Set_Number_5,_Problem_3_,  (myself)
-- 
Scott Bostater      GTRI/RAIL/RAD   (Ga. Tech)
"My soul finds rest in God alone; my salvation comes from Him"  -Ps 62.1
uucp:     ...!{allegra,amd,hplabs,ut-ngp}!gatech!prism!bb16
Internet: bb16@prism.gatech.edu