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Statistics::Descriptive(3pm) User Contributed Perl Documentation Statistics::Descriptive(3pm)
NAME
Statistics::Descriptive - Module of basic descriptive statistical functions.
SYNOPSIS
use Statistics::Descriptive;
$stat = Statistics::Descriptive::Full->new();
$stat->add_data(1,2,3,4); $mean = $stat->mean();
$var = $stat->variance();
$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->get_data();
Returns a copy of the data array.
$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.
$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.
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:
<http://www.ietf.org/rfc/rfc2330.txt> .)
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
Exemple :
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.
$stat->mode();
Returns the mode of the data.
$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, <http://www.shlomifish.org/> , "shlomif AT cpan.org"
Previously:
Colin Kuskie
My email address can be found at http://www.perl.com under Who's Who or at:
http://search.cpan.org/author/COLINK/.
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.
REVISION HISTORY
v2.3
Rolled into November 1998
Code provided by Andrea Spinelli to prevent division by zero and to make consistent
return values for undefined behavior. Andrea also provided a test bench for the
module.
A bug fix for the calculation of frequency distributions. Thanks to Nick Tolli for
alerting this to me.
Added 4 lines of code to Makefile.PL to make it easier for the ActiveState
installation tool to use. Changes work fine in perl5.004_04, haven't tested them
under perl5.005xx yet.
v2.2
Rolled into March 1998.
Fixed problem with sending 0's and -1's as data. The old 0 : true ? false thing. Use
defined to fix.
Provided a fix for AUTOLOAD/DESTROY/Carp bug. Very strange.
v2.1
August 1997
Fixed errors in statistics algorithms caused by changing the interface.
v2.0
August 1997
Fixed errors in removing cached values (they weren't being removed!) and added
sort_data and presorted methods.
June 1997
Transferred ownership of the module from Jason to Colin.
Rewrote OO interface, modified function distribution, added mindex, maxdex.
v1.1
April 1995
Added LeastSquaresFit and FrequencyDistribution.
v1.0
March 1995
Released to comp.lang.perl and placed on archive sites.
v.20
December 1994
Complete rewrite after extensive and invaluable e-mail correspondence with Anno
Siegel.
v.10
December 1994
Initital concept, released to perl5-porters list.
perl v5.10.0 2009-07-20 Statistics::Descriptive(3pm)
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On Apache
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2012-05-25 02:12 @38.107.179.237 Crawled by CCBot/1.0 (+http://www.commoncrawl.org/bot.html)