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 (PDFs).

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.