Statistics::Descriptive::Sparse(3pm) User Contributed Perl Documentation
NAME
Statistics::Descriptive - Module of basic descriptive statistical
functions.
VERSION
version 3.0801
SYNOPSIS
use Statistics::Descriptive;
my $stat = Statistics::Descriptive::Full->new();
$stat->add_data(1,2,3,4);
my $mean = $stat->mean();
my $var = $stat->variance();
my $tm = $stat->trimmed_mean(.25);
$Statistics::Descriptive::Tolerance = 1e-10;
DESCRIPTION
This module provides basic functions used in descriptive statistics.
It has an object oriented design and supports two different types of
data storage and calculation objects: sparse and full. With the sparse
method, none of the data is stored and only a few statistical measures
are available. Using the full method, the entire data set is retained
and additional functions are available.
Whenever a division by zero may occur, the denominator is checked to be
greater than the value $Statistics::Descriptive::Tolerance, which
defaults to 0.0. You may want to change this value to some small
positive value such as 1e-24 in order to obtain error messages in case
of very small denominators.
Many of the methods (both Sparse and Full) cache values so that
subsequent calls with the same arguments are faster.
METHODS
Sparse Methods
$stat = Statistics::Descriptive::Sparse->new();
Create a new sparse statistics object.
$stat->clear();
Effectively the same as
my $class = ref($stat);
undef $stat;
$stat = new $class;
except more efficient.
$stat->add_data(1,2,3);
Adds data to the statistics variable. The cached statistical
values are updated automatically.
$stat->count();
Returns the number of data items.
$stat->mean();
Returns the mean of the data.
$stat->sum();
Returns the sum of the data.
$stat->variance();
Returns the variance of the data. Division by n-1 is used.
$stat->standard_deviation();
Returns the standard deviation of the data. Division by n-1 is
used.
$stat->min();
Returns the minimum value of the data set.
$stat->mindex();
Returns the index of the minimum value of the data set.
$stat->max();
Returns the maximum value of the data set.
$stat->maxdex();
Returns the index of the maximum value of the data set.
$stat->sample_range();
Returns the sample range (max - min) of the data set.
Full Methods
Similar to the Sparse Methods above, any Full Method that is called
caches the current result so that it doesn't have to be recalculated.
In some cases, several values can be cached at the same time.
$stat = Statistics::Descriptive::Full->new();
Create a new statistics object that inherits from
Statistics::Descriptive::Sparse so that it contains all the
methods described above.
$stat->add_data(1,2,4,5);
Adds data to the statistics variable. All of the sparse
statistical values are updated and cached. Cached values from
Full methods are deleted since they are no longer valid.
Note: Calling add_data with an empty array will delete all of
your Full method cached values! Cached values for the sparse
methods are not changed
$stat->add_data_with_samples([{1 => 10}, {2 => 20}, {3 => 30},]);
Add data to the statistics variable and set the number of samples
each value has been built with. The data is the key of each
element of the input array ref, while the value is the number of
samples: [{data1 => smaples1}, {data2 => samples2}, ...].
NOTE: The number of samples is only used by the smoothing function
and is ignored otherwise. It is not equivalent to repeat count. In
order to repeat a certain datum more than one time call add_data()
like this:
my $value = 5;
my $repeat_count = 10;
$stat->add_data(
[ ($value) x $repeat_count ]
);
$stat->get_data();
Returns a copy of the data array.
$stat->get_data_without_outliers();
Returns a copy of the data array without outliers. The number
minimum of samples to apply the outlier filtering is
$Statistics::Descriptive::Min_samples_number, 4 by default.
A function to detect outliers need to be defined (see
"set_outlier_filter"), otherwise the function will return an undef
value.
The filtering will act only on the most extreme value of the data
set (i.e.: value with the highest absolute standard deviation from
the mean).
If there is the need to remove more than one outlier, the
filtering need to be re-run for the next most extreme value with
the initial outlier removed.
This is not always needed since the test (for example Grubb's
test) usually can only detect the most exreme value. If there is
more than one extreme case in a set, then the standard deviation
will be high enough to make neither case an outlier.
$stat->set_outlier_filter($code_ref);
Set the function to filter out the outlier.
$code_ref is the reference to the subroutine implementing the
filtering function.
Returns "undef" for invalid values of $code_ref (i.e.: not defined
or not a code reference), 1 otherwise.
o Example #1: Undefined code reference
my $stat = Statistics::Descriptive::Full->new();
$stat->add_data(1, 2, 3, 4, 5);
print $stat->set_outlier_filter(); # => undef
o Example #2: Valid code reference
sub outlier_filter { return $_[1] > 1; }
my $stat = Statistics::Descriptive::Full->new();
$stat->add_data( 1, 1, 1, 100, 1, );
print $stat->set_outlier_filter( \&outlier_filter ); # => 1
my @filtered_data = $stat->get_data_without_outliers();
# @filtered_data is (1, 1, 1, 1)
In this example the series is really simple and the outlier
filter function as well. For more complex series the outlier
filter function might be more complex (see Grubbs' test for
outliers).
The outlier filter function will receive as first parameter
the Statistics::Descriptive::Full object, as second the value
of the candidate outlier. Having the object in the function
might be useful for complex filters where statistics property
are needed (again see Grubbs' test for outlier).
$stat->set_smoother({ method => 'exponential', coeff => 0, });
Set the method used to smooth the data and the smoothing
coefficient. See "Statistics::Smoother" for more details.
$stat->get_smoothed_data();
Returns a copy of the smoothed data array.
The smoothing method and coefficient need to be defined (see
"set_smoother"), otherwise the function will return an undef
value.
$stat->sort_data();
Sort the stored data and update the mindex and maxdex methods.
This method uses perl's internal sort.
$stat->presorted(1);
$stat->presorted();
If called with a non-zero argument, this method sets a flag that
says the data is already sorted and need not be sorted again.
Since some of the methods in this class require sorted data, this
saves some time. If you supply sorted data to the object, call
this method to prevent the data from being sorted again. The flag
is cleared whenever add_data is called. Calling the method
without an argument returns the value of the flag.
$stat->skewness();
Returns the skewness of the data. A value of zero is no skew,
negative is a left skewed tail, positive is a right skewed tail.
This is consistent with Excel.
$stat->kurtosis();
Returns the kurtosis of the data. Positive is peaked, negative is
flattened.
$x = $stat->percentile(25);
($x, $index) = $stat->percentile(25);
Sorts the data and returns the value that corresponds to the
percentile as defined in RFC2330:
o For example, given the 6 measurements:
-2, 7, 7, 4, 18, -5
Then F(-8) = 0, F(-5) = 1/6, F(-5.0001) = 0, F(-4.999) = 1/6,
F(7) = 5/6, F(18) = 1, F(239) = 1.
Note that we can recover the different measured values and how
many times each occurred from F(x) -- no information regarding
the range in values is lost. Summarizing measurements using
histograms, on the other hand, in general loses information
about the different values observed, so the EDF is preferred.
Using either the EDF or a histogram, however, we do lose
information regarding the order in which the values were
observed. Whether this loss is potentially significant will
depend on the metric being measured.
We will use the term "percentile" to refer to the smallest
value of x for which F(x) >= a given percentage. So the 50th
percentile of the example above is 4, since F(4) = 3/6 = 50%;
the 25th percentile is -2, since F(-5) = 1/6 < 25%, and F(-2)
= 2/6 >= 25%; the 100th percentile is 18; and the 0th
percentile is -infinity, as is the 15th percentile, which for
ease of handling and backward compatibility is returned as
undef() by the function.
Care must be taken when using percentiles to summarize a
sample, because they can lend an unwarranted appearance of
more precision than is really available. Any such summary
must include the sample size N, because any percentile
difference finer than 1/N is below the resolution of the
sample.
(Taken from: RFC2330 - Framework for IP Performance Metrics,
Section 11.3. Defining Statistical Distributions. RFC2330 is
available from: .)
If the percentile method is called in a list context then it will
also return the index of the percentile.
$x = $stat->quantile($Type);
Sorts the data and returns estimates of underlying distribution
quantiles based on one or two order statistics from the supplied
elements.
This method use the same algorithm as Excel and R language
(quantile type 7).
The generic function quantile produces sample quantiles
corresponding to the given probabilities.
$Type is an integer value between 0 to 4 :
0 => zero quartile (Q0) : minimal value
1 => first quartile (Q1) : lower quartile = lowest cut off (25%) of data = 25th percentile
2 => second quartile (Q2) : median = it cuts data set in half = 50th percentile
3 => third quartile (Q3) : upper quartile = highest cut off (25%) of data, or lowest 75% = 75th percentile
4 => fourth quartile (Q4) : maximal value
Example :
my @data = (1..10);
my $stat = Statistics::Descriptive::Full->new();
$stat->add_data(@data);
print $stat->quantile(0); # => 1
print $stat->quantile(1); # => 3.25
print $stat->quantile(2); # => 5.5
print $stat->quantile(3); # => 7.75
print $stat->quantile(4); # => 10
$stat->median();
Sorts the data and returns the median value of the data.
$stat->harmonic_mean();
Returns the harmonic mean of the data. Since the mean is
undefined if any of the data are zero or if the sum of the
reciprocals is zero, it will return undef for both of those cases.
$stat->geometric_mean();
Returns the geometric mean of the data.
my $mode = $stat->mode();
Returns the mode of the data. The mode is the most commonly
occurring datum. See
. If all
values occur only once, then mode() will return undef.
$stat->sumsq()
The sum of squares.
$stat->trimmed_mean(ltrim[,utrim]);
trimmed_mean(ltrim) returns the mean with a fraction "ltrim" of
entries at each end dropped. "trimmed_mean(ltrim,utrim)" returns
the mean after a fraction "ltrim" has been removed from the lower
end of the data and a fraction "utrim" has been removed from the
upper end of the data. This method sorts the data before
beginning to analyze it.
All calls to trimmed_mean() are cached so that they don't have to
be calculated a second time.
$stat->frequency_distribution_ref($partitions);
$stat->frequency_distribution_ref(\@bins);
$stat->frequency_distribution_ref();
frequency_distribution_ref($partitions) slices the data into
$partition sets (where $partition is greater than 1) and counts
the number of items that fall into each partition. It returns a
reference to a hash where the keys are the numerical values of the
partitions used. The minimum value of the data set is not a key
and the maximum value of the data set is always a key. The number
of entries for a particular partition key are the number of items
which are greater than the previous partition key and less then or
equal to the current partition key. As an example,
$stat->add_data(1,1.5,2,2.5,3,3.5,4);
$f = $stat->frequency_distribution_ref(2);
for (sort {$a <=> $b} keys %$f) {
print "key = $_, count = $f->{$_}\n";
}
prints
key = 2.5, count = 4
key = 4, count = 3
since there are four items less than or equal to 2.5, and 3 items
greater than 2.5 and less than 4.
frequency_distribution_refs(\@bins) provides the bins that are to
be used for the distribution. This allows for non-uniform
distributions as well as trimmed or sample distributions to be
found. @bins must be monotonic and contain at least one element.
Note that unless the set of bins contains the range that the total
counts returned will be less than the sample size.
Calling frequency_distribution_ref() with no arguments returns the
last distribution calculated, if such exists.
my %hash = $stat->frequency_distribution($partitions);
my %hash = $stat->frequency_distribution(\@bins);
my %hash = $stat->frequency_distribution();
Same as frequency_distribution_ref() except that returns the hash
clobbered into the return list. Kept for compatibility reasons
with previous versions of Statistics::Descriptive and using it is
discouraged.
$stat->least_squares_fit();
$stat->least_squares_fit(@x);
least_squares_fit() performs a least squares fit on the data,
assuming a domain of @x or a default of 1..$stat->count(). It
returns an array of four elements "($q, $m, $r, $rms)" where
"$q and $m"
satisfy the equation C($y = $m*$x + $q).
$r is the Pearson linear correlation cofficient.
$rms
is the root-mean-square error.
If case of error or division by zero, the empty list is returned.
The array that is returned can be "coerced" into a hash structure
by doing the following:
my %hash = ();
@hash{'q', 'm', 'r', 'err'} = $stat->least_squares_fit();
Because calling least_squares_fit() with no arguments defaults to
using the current range, there is no caching of the results.
REPORTING ERRORS
I read my email frequently, but since adopting this module I've added 2
children and 1 dog to my family, so please be patient about my response
times. When reporting errors, please include the following to help me
out:
o Your version of perl. This can be obtained by typing perl "-v" at
the command line.
o Which version of Statistics::Descriptive you're using. As you can
see below, I do make mistakes. Unfortunately for me, right now
there are thousands of CD's with the version of this module with
the bugs in it. Fortunately for you, I'm a very patient module
maintainer.
o Details about what the error is. Try to narrow down the scope of
the problem and send me code that I can run to verify and track it
down.
AUTHOR
Current maintainer:
Shlomi Fish, , "shlomif@cpan.org"
Previously:
Colin Kuskie
My email address can be found at http://www.perl.com under Who's Who or
at: https://metacpan.org/author/COLINK .
CONTRIBUTORS
Fabio Ponciroli & Adzuna Ltd. team (outliers handling)
REFERENCES
RFC2330, Framework for IP Performance Metrics
The Art of Computer Programming, Volume 2, Donald Knuth.
Handbook of Mathematica Functions, Milton Abramowitz and Irene Stegun.
Probability and Statistics for Engineering and the Sciences, Jay
Devore.
COPYRIGHT
Copyright (c) 1997,1998 Colin Kuskie. All rights reserved. This
program is free software; you can redistribute it and/or modify it
under the same terms as Perl itself.
Copyright (c) 1998 Andrea Spinelli. All rights reserved. This program
is free software; you can redistribute it and/or modify it under the
same terms as Perl itself.
Copyright (c) 1994,1995 Jason Kastner. All rights reserved. This
program is free software; you can redistribute it and/or modify it
under the same terms as Perl itself.
LICENSE
This program is free software; you can redistribute it and/or modify it
under the same terms as Perl itself.
SUPPORT
Websites
The following websites have more information about this module, and may
be of help to you. As always, in addition to those websites please use
your favorite search engine to discover more resources.
o MetaCPAN
A modern, open-source CPAN search engine, useful to view POD in
HTML format.
o RT: CPAN's Bug Tracker
The RT ( Request Tracker ) website is the default bug/issue
tracking system for CPAN.
o CPANTS
The CPANTS is a website that analyzes the Kwalitee ( code metrics )
of a distribution.
o CPAN Testers
The CPAN Testers is a network of smoke testers who run automated
tests on uploaded CPAN distributions.
o CPAN Testers Matrix
The CPAN Testers Matrix is a website that provides a visual
overview of the test results for a distribution on various
Perls/platforms.
o CPAN Testers Dependencies
The CPAN Testers Dependencies is a website that shows a chart of
the test results of all dependencies for a distribution.
Bugs / Feature Requests
Please report any bugs or feature requests by email to
"bug-statistics-descriptive at rt.cpan.org", or through the web
interface at
.
You will be automatically notified of any progress on the request by
the system.
Source Code
The code is open to the world, and available for you to hack on. Please
feel free to browse it and play with it, or whatever. If you want to
contribute patches, please send me a diff or prod me to pull from your
repository :)
git clone git://github.com/shlomif/perl-Statistics-Descriptive.git
AUTHOR
Shlomi Fish
BUGS
Please report any bugs or feature requests on the bugtracker website
When submitting a bug or request, please include a test-file or a patch
to an existing test-file that illustrates the bug or desired feature.
COPYRIGHT AND LICENSE
This software is copyright (c) 1997 by Jason Kastner, Andrea Spinelli,
Colin Kuskie, and others.
This is free software; you can redistribute it and/or modify it under
the same terms as the Perl 5 programming language system itself.
perl v5.38.2 2024-07-13
Statistics::Descriptive::Sparse(3pm)