NAME

       Statistics::Test::RandomWalk - Random Walk test for random numbers

SYNOPSIS

         use Statistics::Test::RandomWalk;
         my $tester = Statistics::Test::RandomWalk->new();
         $tester->set_data( [map {rand()} 1..1000000] );

         my $no_bins = 10;
         my ($quant, $got, $expected) = $tester->test($no_bins);
         print $tester->data_to_report($quant, $got, $expected);

DESCRIPTION

       This module implements a Random Walk test of a random number generator as outlined in
       Blobel et al (Refer to the SEE ALSO section).

       Basically, it tests that the numbers "[0,1]" generated by a random number generator are
       distributed evenly. It divides "[0,1]" into "n" evenly sized bins and calculates the
       number of expected and actual random numbers in the bin. (In fact, this counts the
       cumulated numbers, but that works the same.)

METHODS

   new
       Creates a new random number tester.

   set_rescale_factor
       The default range of the random numbers [0, 1) can be rescaled by a constant factor. This
       method is the setter for that factor.

   rescale_factor
       Returns the current rescaling factor.

   set_data
       Sets the random numbers to operate on. First argument must be either an array reference to
       an array of random numbers or a code reference.

       If the first argument is a code reference, the second argument must be an integer "n". The
       code reference is called "n"-times and its return values are used as random numbers.

       The code reference semantics are particularly useful if you do not want to store all
       random numbers in memory at the same time. You can write a subroutine that, for example,
       generates and returns batches of 100 random numbers so no more than 101 of these numbers
       will be in memory at the same time. Note that if you return 100 numbers at once and pass
       in "n=50", you will have a sequence of 5000 random numbers.

   test
       Runs the Random Walk test on the data that was previously set using "set_data".

       First argument must be the number of bins.

       Returns three array references. First is an array of quantiles.  If the number of bins was
       ten, this (and all other returned arrays) will hold ten items.

       Second are the determined numbers of random numbers below the quantiles. Third are the
       expected counts.

   data_to_report
       From the data returned by the "test()" method, this method creates a textual report and
       returns it as a string.

       Do not forget to pass in the data that was returned by "test()" or use the "test_report()"
       method directly if you do not use the data otherwise.

SUBROUTINES

   n_over_k
       Computes "n" over "k". Uses Perl's big number support and returns a Math::BigFloat object.

       This sub is memoized.

SEE ALSO

       Math::BigFloat, Memoize, Params::Util

       Random number generators: Math::Random::MT, Math::Random, Math::Random::OO,
       Math::TrulyRandom, "/dev/random" where available

       Statistics::Test::Sequence

       The algorithm was taken from: (German)

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

AUTHOR

       Steffen Mueller, <smueller@cpan.org>

COPYRIGHT AND LICENSE

       Copyright (C) 2007-2010 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.