Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
1991
*January
*February
*March
*August
*September
*October
*November
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 1991

[Date Index] [Thread Index] [Author Index]

Search the Archive

RE: Generating a normal 0,1

  • To: mathgroup at yoda.ncsa.uiuc.edu
  • Subject: RE: Generating a normal 0,1
  • From: blachman%gtewd.dnet at gte.com (NELSON M. BLACHMAN)
  • Date: Wed, 23 Jan 91 17:11:49 -0500

  Generating a single standard normal random variable x is somewhat hard and 
slow, but generating two independent ones, x and y, is easy.

  Let u and v be two independent reals distributed uniformly between 0 and 1.  
Then   
		x = Sqrt[-2 Log[u]] Cos[2 Pi v]  
and  
		y = Sqrt[-2 Log[u]] Sin[2 Pi v]  

are independent zero-mean normal random variables with unit variance.  

  This is established by noticing that the angle ArcTan[y/x] must have a 
uniform distribution like v/(2 Pi), and r = Sqrt[x^2 + y^2] must have a 
Rayleigh distribution with cumulative distribution function  1 - E^(-r^2/2), 
which can be set equal to 1 - u.

					Nelson M. Blachman
					GTE Government Systems Corp.
					Mountain View, California
					blachman%gtewd.dnet at gte.com


  • Prev by Date: Integrals of Bessel functions
  • Next by Date: Controlling evaluation or Re: Plot[] acting funny (help)
  • Previous by thread: Integrals of Bessel functions
  • Next by thread: Controlling evaluation or Re: Plot[] acting funny (help)