Francesco Nidito

# NAME

Statistics::OnLine - Pure Perl implementation of the on-line algorithm to produce statistics

# SYNOPSIS

 use Statistics::OnLine;
my $s = Statistics::OnLine->new; my @data = (1, 2, 3, 4, 5);$s->add_data( @data );
$s->add_data( 6, 7 );$s->add_data( 8 );

print "count = ",$s->count,"\tmean = ",$s->mean,"\tvariance = ",$s->variance,"\tvariance_n = ",$s->variance_n,"\tskewness = ",$s->skewness,"\tkurtosis = ",$s->kurtosis,"\n";

$s->add_data( ); # does nothing! print "count = ",$s->count,"\tmean = ",$s->mean,"\tvariance = ",$s->variance,"\tvariance_n = ",
$s->variance_n,"\tskewness = ",$s->skewness,"\tkurtosis = ",$s->kurtosis,"\n";$s->add_data( 9, 10 );
print "count = ",$s->count,"\tmean = ",$s->mean,"\tvariance = ",$s->variance,"\tvariance_n = ",$s->variance_n,"\tskewness = ",$s->skewness,"\tkurtosis = ",$s->kurtosis,"\n";

# DESCRIPTION

This module implements a tool to perform statistic operations on large datasets which, typically, could not fit the memory of the machine, e.g. a stream of data from the network.

Once instantiated, an object of the class provide an add_data method to add data to the dataset. When the computation of some statistics is required, at some point of the stream, the appropriate method can be called. After the execution of the statistics it is possible to continue to add new data. In turn, the object will continue to update the existing data to provide new statistics.

# METHODS

new()

Creates a new Statistics::OnLine object and returns it.

add_data(@)

Adds new data to the object and updates the internal state of the statistics.

The method return the object itself in order to use it in chaining:

 my $v =$s->add_data( 1, 2, 3, 4 )->variance;
clean()

Cleans the internal state of the object and resets all the internal statistics.

Return the object itself in order to use it in chaining:

 my $v =$s->clean->add_data( 1, 2, 3, 4 )->variance;
count()

Returns the actual number or elements inserted and processed by the object.

mean()

Returns the average of the elements inserted into the system:

 \fract{ \sum_1^n{x_i} }{ n }
variance()

Returns the variance of the element inserted into the system:

 \fract{ \sum_1^n{avg - x_i} }{ n - 1 }
variance_n()

Returns the variance of the element inserted into the system:

 \fract{ \sum_1^n{avg - x_i} }{ n }
skewness()

Returns the skewness (third standardized moment) of the element inserted into the system http://en.wikipedia.org/wiki/Skewness

kurtosis()

Returns the kurtosis (fourth standardized moment) of the element inserted into the system http://en.wikipedia.org/wiki/Kurtosis

# ERROR MESSAGES

The conditions in which the system can return errors, using a die are:

too few elements to compute function

Some functions need a minimum number of elements to be computed: mean, variance_n and skewness need at least one element, variance at least two and kurtosis needs at least four.

variance is zero: cannot compute kurtosis|skewness

Both kurtosis and skewness need that variance to be greater than zero.

# THEORY

On-line statistics are based on strong mathematical foundations which transform the standard computations into a sequence of operations that incrementally update with new values the actual ones.

There are some referencence in the web. This documentation suggest to start your investigation from http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Higher-order_statistics. The linked page provides other useful references on the foundations of the method.

# CAVEAT

The module is intended to be used in all the situations in which: (1) the number of data elements could be too large with respect the memory of the system, or (2) the elements arrive at different time stamps and intermediate results are needed.

If the length of the stream is fixed, all the data elements are present in a single place and there is not need for intermediate results, it could be better to use different modules, for instance Statistics::Lite, to make computations.

The reason for this choice is that the module uses a stable approximation, well suited for the use on steams (effectively an on-line algorithm). Using this system on fixed datasets could introduce some (little) approximation.

# HISTORY

0.02

Corrected typos in documentation

0.01

Initial version of the module

# AUTHOR

Francesco Nidito

Copyright 2009 Francesco Nidito. All rights reserved.

This library is free software; you can redistribute it and/or modify it under the same terms as Perl itself.