NAME
Statistics::Running::Tiny - Basic descriptive statistics
(mean/stdev/min/max/skew/kurtosis) over data without the need to store
data points ever. OOP style. The Tiny version.
VERSION
Version 0.04
SYNOPSIS
use Statistics::Running::Tiny;
my $ru = Statistics::Running::Tiny->new();
for(1..100){
$ru->add(rand());
}
print "mean: ".$ru->mean()."\n";
$ru->add(12345);
print "mean: ".$ru->mean()."\n";
my $ru2 = Statistics::Running::Tiny->new();
for(1..100){
$ru2->add(rand());
}
my $ru3 = $ru + $ru2;
print "mean of concatenated data: ".$ru3->mean()."\n";
$ru += $ru2;
print "mean after appending data: ".$ru->mean()."\n";
print "stats: ".$ru->stringify()."\n";
DESCRIPTION
Calculate basic descriptive statistics (mean, variance, standard
deviation, skewness, kurtosis) without the need to store any data
point/sample. Statistics are updated each time a new data point/sample
comes in.
There are three amazing things about B.P.Welford's algorithm
implemented here:
1. It calculates and keeps updating mean/standard-deviation etc. on
data without the need to store that data. As new data comes in, the
statistics are updated based on the state of a few variables (mean,
number of data points, etc.) but not the past data points. This
includes the calculation of standard deviation which most of us knew
(wrongly) that it requires a second pass on the data points, after the
mean is calculated. Well, B.P.Welford found a way to avoid this.
2. The standard formula for standard deviation requires to sum the
square of the difference of each sample from the mean. If samples are
large numbers then you are summing differences of large numbers. If
further there is little difference between samples, and the discrepancy
from the mean is small, then you are prone to precision errors which
accumulate to destructive effect if the number of samples is large. In
contrast, B.P.Welford's algorithm does not suffer from this, it is
stable and accurate.
3. B.P.Welford's online statistics algorithm is quite a revolutionary
idea and why is not an obligatory subject in first-year programming
courses is beyond comprehension. Here is a way to decrease those CO2
emissions.
The basis for the code in this module is from John D. Cook's article
and C++ implementation
EXPORT
Nothing, this is an Object Oriented module. Once you instantiate an
object all its methods are yours.
SUBROUTINES/METHODS
new
Constructor, initialises internal variables.
add
Update our statistics after one more data point/sample (or an array of
them) is presented to us.
my $ru1 = Statistics::Running::Tiny->new();
for(1..100){
$ru1->add(rand());
print $ru1."\n";
}
Input can be a single data point (a scalar) or a reference to an array
of data points.
copy_from
Copy state of input object into current effectively making us like
them. Our previous state is forgotten. After that adding a new data
point into us will be with the new state copied.
my $ru1 = Statistics::Running::Tiny->new();
for(1..100){
$ru1->add(rand());
}
my $ru2 = Statistics::Running::Tiny->new();
for(1..100){
$ru2->add(rand(1000000));
}
# copy the state of ru1 into ru2. state of ru1 is forgotten.
$ru2->copy_from($ru1);
clone
Clone state of our object into a newly created object which is
returned. Our object and returned object are identical at the time of
cloning.
my $ru1 = Statistics::Running::Tiny->new();
for(1..100){
$ru1->add(rand(1000000));
}
my $ru2 = $ru1->clone();
clear
Clear our internal state as if no data points have ever added into us.
As if we were just created. All state is forgotten and reset to zero.
mean
Returns the mean of all the data pushed in us
sum
Returns the sum of all the data pushed in us (algebraic sum, not
absolute sum)
abs_sum
Returns the sum of the absolute value of all the data pushed in us
(this is not algebraic sum)
min
Returns the minimum data sample added in us
max
Returns the maximum data sample added in us
get_N
Returns the number of data points/samples inserted, and had their
descriptive statistics calculated, so far.
variance
Returns the variance of the data points/samples added onto us so far.
standard_deviation
Returns the standard deviation of the data points/samples added onto us
so far. This is the square root of the variance.
skewness
Returns the skewness of the data points/samples added onto us so far.
kurtosis
Returns the kurtosis of the data points/samples added onto us so far.
concatenate
Concatenates our state with the input object's state and returns a
newly created object with the combined state. Our object and input
object are not modified. The overloaded symbol '+' points to this sub.
append
Appends input object's state into ours. Our state is modified. (input
object's state is not modified) The overloaded symbol '+=' points to
this sub.
equals
Check if our state (number of samples and all internal state) is the
same with input object's state. Equality here implies that ALL
statistics are equal (within a small number
Statistics::Running::Tiny::SMALL_NUMBER_FOR_EQUALITY)
equals_statistics
Check if our statistics only (and not sample size) are the same with
input object. E.g. it checks mean, variance etc. but not sample size
(as with the real equals()). It returns 0 on non-equality. 1 if equal.
stringify
Returns a string description of descriptive statistics we know about
(mean, standard deviation, kurtosis, skewness) as well as the number of
data points/samples added onto us so far. Note that this method is not
necessary because stringification is overloaded and the follow print
$stats_obj."\n" is equivalent to print $stats_obj->stringify()."\n"
Overloaded functionality
1. Addition of two statistics objects: my $ru3 = $ru1 + $ru2
2. Test for equality: if( $ru2 == $ru3 ){ ... }
3. Stringification: print $ru1."\n"
Testing for Equality
In testing if two objects are the same, their means, standard
deviations etc. are compared. This is done using if( ($self->mean() -
$other->mean()) < Statistics::Running::SMALL_NUMBER_FOR_EQUALITY ){ ...
}
BENCHMARKS
Run make bench for benchmarks which report the maximum number of data
points inserted per second (in your system).
SEE ALSO
1. Wikipedia
2. John D. Cook's article and C++ implementation
was used both as
inspiration and as the basis for the formulas for kurtosis() and
skewness()
3. Statistics::Welford This module does not provide kurtosis() and
skewness() which current module does.
4. Statistics::Running This is the exact same module with the addition
of a histogram logging each inserted data point. The histogram is in
effect a discrete approximation of the Probability Distribution of the
input data points. The current module is the same as that bar the
histogram. That makes it a bit faster. Check make bench for benchmarks
AUTHOR
Andreas Hadjiprocopis,
BUGS
Please report any bugs or feature requests to bug-statistics-running at
rt.cpan.org, or through the web interface at
http://rt.cpan.org/NoAuth/ReportBug.html?Queue=Statistics-Running. I
will be notified, and then you'll automatically be notified of progress
on your bug as I make changes.
SUPPORT
You can find documentation for this module with the perldoc command.
perldoc Statistics::Running::Tiny
You can also look for information at:
* RT: CPAN's request tracker (report bugs here)
http://rt.cpan.org/NoAuth/Bugs.html?Dist=Statistics-Running
* AnnoCPAN: Annotated CPAN documentation
http://annocpan.org/dist/Statistics-Running
* Review this module at PerlMonks
https://www.perlmonks.org/?node_id=21144
* Search CPAN
http://search.cpan.org/dist/Statistics-Running/
DEDICATIONS
Almaz
ACKNOWLEDGEMENTS
B.P.Welford, John Cook.
LICENSE AND COPYRIGHT
Copyright 2018-2019 Andreas Hadjiprocopis.
This program is free software; you can redistribute it and/or modify it
under the terms of the the Artistic License (2.0). You may obtain a
copy of the full license at:
http://www.perlfoundation.org/artistic_license_2_0
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