/ 
Statistics-Running-Tiny-0.01
River stage zero No dependents
/ Statistics::Running::Tiny

NAME

Statistics::Running::Tiny - Basic descriptive statistics (incl. min/max/skew/kurtosis) without the need to store data points, statistics are updated every time a new data point is added in

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.

VERSION

Version 0.01

SYNOPSIS

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 at

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";

EXPORT

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->stringify()."\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.

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 processed (added onto us) 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.

BENCHMARKS

Check make bench for benchmarks

SEE ALSO

1. Wikipedia
2. John D. Cook's article and C++ implementation at
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, <bliako at cpan.org>

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:

ACKNOWLEDGEMENTS

LICENSE AND COPYRIGHT

Copyright 2018 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

Any use, modification, and distribution of the Standard or Modified Versions is governed by this Artistic License. By using, modifying or distributing the Package, you accept this license. Do not use, modify, or distribute the Package, if you do not accept this license.

If your Modified Version has been derived from a Modified Version made by someone other than you, you are nevertheless required to ensure that your Modified Version complies with the requirements of this license.

This license does not grant you the right to use any trademark, service mark, tradename, or logo of the Copyright Holder.

This license includes the non-exclusive, worldwide, free-of-charge patent license to make, have made, use, offer to sell, sell, import and otherwise transfer the Package with respect to any patent claims licensable by the Copyright Holder that are necessarily infringed by the Package. If you institute patent litigation (including a cross-claim or counterclaim) against any party alleging that the Package constitutes direct or contributory patent infringement, then this Artistic License to you shall terminate on the date that such litigation is filed.

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