Delila Program: normal

normal program

Documentation for the normal program is below, with links to related programs in the "see also" section.

{version = 3.17; (* of normal.p 1994 sep 5}

(* begin module describe.normal *)
(*
name
   normal: generate normally distributed random numbers

synopsis
   normal(normalp:in, data: out, output: out)

files
   normalp: parameter file controlling the program.
      Two numbers, one per line:
         seed: random seed to start the process
         total: the number of numbers to generate
   data: This is a set of numbers which should have Gaussian distribution
      if the random number generator is a reasonable one.
      It will be N(0,1), a normal distribution
      with mean 0 and standard deviation 1.
   genhisp: control file for the genhis histogram plotting program.
   output: messages to the user

description
   Test of a random number generator by creating a gaussian
   distribution of numbers for plotting by genhis.
   Method: if U is a member of the set [0..1] and Un and Un+1
   are two members, then define
      theta = Un 2 pi
      r     = sqrt(-2 ln(Un+1))
   then when these polar coordinates are converted to Cartesian
   coordinates, one gets two independent Normally distributed numbers,
   with mean 0 and standard deviation 1.  To get other standard deviations
   multiply by a constant, and to get other means, add a constant.

   The proof was from a friend; I only have sketch notes at the moment.
   I'm sure it is available in standard texts.  However, it works,
   as shown by the example.

example
  seed := 0.5;
  total := 10000;
     The mean was 0.00 (to two places) and the standard deviation was 1.01.

see also
   gentst.p, tstrnd.p, genhis.p

author
  Tom Schneider
  National Cancer Institute
  Laboratory of Mathematical Biology
  Frederick, Maryland
  toms@ncifcrf.gov

bugs
   none known

*)
(* end module describe.normal *)
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