NAME
Statistics::OnLine  Pure Perl implementation of the online 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
andskewness
need at least one element,variance
at least two andkurtosis
needs at least four.  variance is zero: cannot compute kurtosisskewness

Both kurtosis and skewness need that variance to be greater than zero.
THEORY
Online 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#Higherorder_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 online algorithm). Using this system on fixed datasets could introduce some (little) approximation.
HISTORY
AUTHOR
Francesco Nidito
COPYRIGHT
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.
SEE ALSO
Statistics::Lite, http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Higherorder_statistics