Math::Random::Cauchy - Random numbers following a Cauchy PDF


  use Math::Random::Cauchy;
  my $cauchy = Math::Random::Cauchy->new(
    fwhm  => 1,  # the width (full width, half maximum), default==1
    middle => 5, # the expectation value, default==0
    random => 'rand', # use Perl's builtin (default)
  foreach (1..100) {
      my $rnd = $cauchy->rand();
      # ...
  # Use Math::Random::MT instead of bultin rand()
  use Math::Random::MT;
  my $mt = Math::Random::Mt->new($seed);
  $cauchy = Math::Random::Cauchy->new(
    random => sub { $mt->rand() };


This module transforms uniformly spaced random numbers into random numbers that follow the Cauchy Probability Density Function (PDF).

A more general transformation method is implemented in Math::Random::AcceptReject.

The algorithm is from Blobel et al as quoted in the SEE ALSO section below.



Creates a new random number generator. Takes named arguments.

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.
  fwhm:   Full width, half maximum. Defaults to 1.
  middle: Expectation value for x. Defaults to 0.


Returns the next random number of Cauchy PDF.


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

The examples in the examples/ subdirectory of this distribution.

The algorithm was taken from: (German)

Blobel, V., and Lohrmann, E. Statistische und numerische Methoden der Datenanalyse. Stuttgart, Leipzig: Teubner, 1998


Steffen Mueller, <>


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.