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_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 particularily 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,
COPYRIGHT AND LICENSE
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.