NAME
    Math::Random::AcceptReject - Acceptance-Rejection PDF transformations

SYNOPSIS
      use Math::Random::AcceptReject;
      my $pdf = Math::Random::AcceptReject->new(
        xmin   => 0, # defaults to 0
        xmax   => 2, # defaults to 1
        ymax   => 2, # no default!
        pdf    => 'x',    # a triangle from x=0 to x=2 with slope 1
        random => 'rand', # use Perl's builtin (default)
      );
  
      foreach (1..100) {
          my $rnd = $pdf->rand();
          # ...
      }
  
      # Use Math::Random::MT instead of bultin rand()
      # Same target PDF but as Perl code instead of a Math::Symbolic
      # function!
      use Math::Random::MT;
      my $mt = Math::Random::Mt->new($seed);
      $pdf = Math::Random::AcceptReject->new(
        xmax   => 2,
        ymax   => 2,
        pdf    => sub { $_[0] },
        random => sub { $mt->rand() };
      );

DESCRIPTION
    This module implements acceptance-rejection transformations of uniformly
    distributed random numbers to mostly arbitrary probability density
    functions (*PDF*s).

    Note that whereas J. von Neumann's algorithm can transform from
    arbitrary source PDFs arbitrary destination PDFs, this module is
    currently limited to uniform "[0,1]" source PDFs!

METHODS
  new
    Creates a new random number generator. Takes named arguments.

    Mandatory parameters:

      pdf:  The probability density function. This can either be a
            subroutine reference which takes an argument ('x') and
            returns f(x), a Math::Symbolic tree representing f(x) and
            using the variable 'x', or a string which can be parsed
            as such a Math::Symbolic tree.
      ymax: Maximum value of the target PDF f(x) in the x range. This
            max theoretically be safely set to a very large value which
            is much higher than the real maximum of f(x) within
            the range [xmin,xmax]. The efficiency of the algorithm goes
            down with 

    Optional parameters:

      random: The random number generator. Defaults to using Perl's
              rand() function. May be set to either 'rand' for the
              default or a subroutine reference for custom random
              number generators. Expected to return one or more(!)
              random numbers per call.
      xmin:   Minimum value for x. Defaults to 0.
      xmax:   Maximum value for x. Defaults to 1.

  rand
    Returns the next random number of PDF f(x) as specified by the "pdf"
    parameter to "new()".

SEE ALSO
    <http://en.wikipedia.org/wiki/Rejection_sampling>

    Math::Random::MT, Math::Random, Math::Random::OO, Math::TrulyRandom

    Math::Symbolic

    The examples in the examples/ subdirectory of this distribution.

AUTHOR
    Steffen Müller, <smueller@cpan.org>

COPYRIGHT AND LICENSE
    Copyright (C) 2007 by Steffen Müller

    This library is free software; you can redistribute it and/or modify it
    under the same terms as Perl itself, either Perl version 5.6 or, at your
    option, any later version of Perl 5 you may have available.

