# 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 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

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.