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 *)
   normal: generate normally distributed random numbers

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

   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

   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.

  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

  Tom Schneider
  Frederick, Maryland

   none known

(* end module describe.normal *)
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