Math::Random::AcceptReject - Acceptance-Rejection PDF transformations
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() }; );
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 to arbitrary destination PDFs, this module is currently limited to uniform [0,1] source PDFs!
[0,1]
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.
Returns the next random number of PDF f(x) as specified by the pdf parameter to new().
f(x)
pdf
new()
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.
Steffen Mueller, <smueller@cpan.org>
Copyright (C) 2007 by Steffen Mueller
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.
To install Math::Random::AcceptReject, copy and paste the appropriate command in to your terminal.
cpanm
cpanm Math::Random::AcceptReject
CPAN shell
perl -MCPAN -e shell install Math::Random::AcceptReject
For more information on module installation, please visit the detailed CPAN module installation guide.