1Statistics::DescriptiveU(s3e)r Contributed Perl DocumentaSttiaotnistics::Descriptive(3)
2
3
4

NAME

6       Statistics::Descriptive - Module of basic descriptive statistical
7       functions.
8

VERSION

10       version 3.0702
11

SYNOPSIS

13           use Statistics::Descriptive;
14           my $stat = Statistics::Descriptive::Full->new();
15           $stat->add_data(1,2,3,4);
16           my $mean = $stat->mean();
17           my $var = $stat->variance();
18           my $tm = $stat->trimmed_mean(.25);
19           $Statistics::Descriptive::Tolerance = 1e-10;
20

DESCRIPTION

22       This module provides basic functions used in descriptive statistics.
23       It has an object oriented design and supports two different types of
24       data storage and calculation objects: sparse and full. With the sparse
25       method, none of the data is stored and only a few statistical measures
26       are available. Using the full method, the entire data set is retained
27       and additional functions are available.
28
29       Whenever a division by zero may occur, the denominator is checked to be
30       greater than the value $Statistics::Descriptive::Tolerance, which
31       defaults to 0.0. You may want to change this value to some small
32       positive value such as 1e-24 in order to obtain error messages in case
33       of very small denominators.
34
35       Many of the methods (both Sparse and Full) cache values so that
36       subsequent calls with the same arguments are faster.
37

VERSION

39       version 3.0702
40

METHODS

42   Sparse Methods
43       $stat = Statistics::Descriptive::Sparse->new();
44            Create a new sparse statistics object.
45
46       $stat->clear();
47            Effectively the same as
48
49              my $class = ref($stat);
50              undef $stat;
51              $stat = new $class;
52
53            except more efficient.
54
55       $stat->add_data(1,2,3);
56            Adds data to the statistics variable. The cached statistical
57            values are updated automatically.
58
59       $stat->count();
60            Returns the number of data items.
61
62       $stat->mean();
63            Returns the mean of the data.
64
65       $stat->sum();
66            Returns the sum of the data.
67
68       $stat->variance();
69            Returns the variance of the data.  Division by n-1 is used.
70
71       $stat->standard_deviation();
72            Returns the standard deviation of the data. Division by n-1 is
73            used.
74
75       $stat->min();
76            Returns the minimum value of the data set.
77
78       $stat->mindex();
79            Returns the index of the minimum value of the data set.
80
81       $stat->max();
82            Returns the maximum value of the data set.
83
84       $stat->maxdex();
85            Returns the index of the maximum value of the data set.
86
87       $stat->sample_range();
88            Returns the sample range (max - min) of the data set.
89
90   Full Methods
91       Similar to the Sparse Methods above, any Full Method that is called
92       caches the current result so that it doesn't have to be recalculated.
93       In some cases, several values can be cached at the same time.
94
95       $stat = Statistics::Descriptive::Full->new();
96            Create a new statistics object that inherits from
97            Statistics::Descriptive::Sparse so that it contains all the
98            methods described above.
99
100       $stat->add_data(1,2,4,5);
101            Adds data to the statistics variable.  All of the sparse
102            statistical values are updated and cached.  Cached values from
103            Full methods are deleted since they are no longer valid.
104
105            Note:  Calling add_data with an empty array will delete all of
106            your Full method cached values!  Cached values for the sparse
107            methods are not changed
108
109       $stat->add_data_with_samples([{1 => 10}, {2 => 20}, {3 => 30},]);
110            Add data to the statistics variable and set the number of samples
111            each value has been built with. The data is the key of each
112            element of the input array ref, while the value is the number of
113            samples: [{data1 => smaples1}, {data2 => samples2}, ...].
114
115            NOTE: The number of samples is only used by the smoothing function
116            and is ignored otherwise. It is not equivalent to repeat count. In
117            order to repeat a certain datum more than one time call add_data()
118            like this:
119
120                my $value = 5;
121                my $repeat_count = 10;
122                $stat->add_data(
123                    [ ($value) x $repeat_count ]
124                );
125
126       $stat->get_data();
127            Returns a copy of the data array.
128
129       $stat->get_data_without_outliers();
130            Returns a copy of the data array without outliers. The number
131            minimum of samples to apply the outlier filtering is
132            $Statistics::Descriptive::Min_samples_number, 4 by default.
133
134            A function to detect outliers need to be defined (see
135            "set_outlier_filter"), otherwise the function will return an undef
136            value.
137
138            The filtering will act only on the most extreme value of the data
139            set (i.e.: value with the highest absolute standard deviation from
140            the mean).
141
142            If there is the need to remove more than one outlier, the
143            filtering need to be re-run for the next most extreme value with
144            the initial outlier removed.
145
146            This is not always needed since the test (for example Grubb's
147            test) usually can only detect the most exreme value. If there is
148            more than one extreme case in a set, then the standard deviation
149            will be high enough to make neither case an outlier.
150
151       $stat->set_outlier_filter($code_ref);
152            Set the function to filter out the outlier.
153
154            $code_ref is the reference to the subroutine implementing the
155            filtering function.
156
157            Returns "undef" for invalid values of $code_ref (i.e.: not defined
158            or not a code reference), 1 otherwise.
159
160            ·   Example #1: Undefined code reference
161
162                    my $stat = Statistics::Descriptive::Full->new();
163                    $stat->add_data(1, 2, 3, 4, 5);
164
165                    print $stat->set_outlier_filter(); # => undef
166
167            ·   Example #2: Valid code reference
168
169                    sub outlier_filter { return $_[1] > 1; }
170
171                    my $stat = Statistics::Descriptive::Full->new();
172                    $stat->add_data( 1, 1, 1, 100, 1, );
173
174                    print $stat->set_outlier_filter( \&outlier_filter ); # => 1
175                    my @filtered_data = $stat->get_data_without_outliers();
176                    # @filtered_data is (1, 1, 1, 1)
177
178                In this example the series is really simple and the outlier
179                filter function as well.  For more complex series the outlier
180                filter function might be more complex (see Grubbs' test for
181                outliers).
182
183                The outlier filter function will receive as first parameter
184                the Statistics::Descriptive::Full object, as second the value
185                of the candidate outlier. Having the object in the function
186                might be useful for complex filters where statistics property
187                are needed (again see Grubbs' test for outlier).
188
189       $stat->set_smoother({ method => 'exponential', coeff => 0, });
190            Set the method used to smooth the data and the smoothing
191            coefficient.  See "Statistics::Smoother" for more details.
192
193       $stat->get_smoothed_data();
194            Returns a copy of the smoothed data array.
195
196            The smoothing method and coefficient need to be defined (see
197            "set_smoother"), otherwise the function will return an undef
198            value.
199
200       $stat->sort_data();
201            Sort the stored data and update the mindex and maxdex methods.
202            This method uses perl's internal sort.
203
204       $stat->presorted(1);
205       $stat->presorted();
206            If called with a non-zero argument, this method sets a flag that
207            says the data is already sorted and need not be sorted again.
208            Since some of the methods in this class require sorted data, this
209            saves some time.  If you supply sorted data to the object, call
210            this method to prevent the data from being sorted again. The flag
211            is cleared whenever add_data is called.  Calling the method
212            without an argument returns the value of the flag.
213
214       $stat->skewness();
215            Returns the skewness of the data.  A value of zero is no skew,
216            negative is a left skewed tail, positive is a right skewed tail.
217            This is consistent with Excel.
218
219       $stat->kurtosis();
220            Returns the kurtosis of the data.  Positive is peaked, negative is
221            flattened.
222
223       $x = $stat->percentile(25);
224       ($x, $index) = $stat->percentile(25);
225            Sorts the data and returns the value that corresponds to the
226            percentile as defined in RFC2330:
227
228            ·   For example, given the 6 measurements:
229
230                -2, 7, 7, 4, 18, -5
231
232                Then F(-8) = 0, F(-5) = 1/6, F(-5.0001) = 0, F(-4.999) = 1/6,
233                F(7) = 5/6, F(18) = 1, F(239) = 1.
234
235                Note that we can recover the different measured values and how
236                many times each occurred from F(x) -- no information regarding
237                the range in values is lost.  Summarizing measurements using
238                histograms, on the other hand, in general loses information
239                about the different values observed, so the EDF is preferred.
240
241                Using either the EDF or a histogram, however, we do lose
242                information regarding the order in which the values were
243                observed.  Whether this loss is potentially significant will
244                depend on the metric being measured.
245
246                We will use the term "percentile" to refer to the smallest
247                value of x for which F(x) >= a given percentage.  So the 50th
248                percentile of the example above is 4, since F(4) = 3/6 = 50%;
249                the 25th percentile is -2, since F(-5) = 1/6 < 25%, and F(-2)
250                = 2/6 >= 25%; the 100th percentile is 18; and the 0th
251                percentile is -infinity, as is the 15th percentile, which for
252                ease of handling and backward compatibility is returned as
253                undef() by the function.
254
255                Care must be taken when using percentiles to summarize a
256                sample, because they can lend an unwarranted appearance of
257                more precision than is really available.  Any such summary
258                must include the sample size N, because any percentile
259                difference finer than 1/N is below the resolution of the
260                sample.
261
262            (Taken from: RFC2330 - Framework for IP Performance Metrics,
263            Section 11.3.  Defining Statistical Distributions.  RFC2330 is
264            available from: <http://www.ietf.org/rfc/rfc2330.txt> .)
265
266            If the percentile method is called in a list context then it will
267            also return the index of the percentile.
268
269       $x = $stat->quantile($Type);
270            Sorts the data and returns estimates of underlying distribution
271            quantiles based on one or two order statistics from the supplied
272            elements.
273
274            This method use the same algorithm as Excel and R language
275            (quantile type 7).
276
277            The generic function quantile produces sample quantiles
278            corresponding to the given probabilities.
279
280            $Type is an integer value between 0 to 4 :
281
282              0 => zero quartile (Q0) : minimal value
283              1 => first quartile (Q1) : lower quartile = lowest cut off (25%) of data = 25th percentile
284              2 => second quartile (Q2) : median = it cuts data set in half = 50th percentile
285              3 => third quartile (Q3) : upper quartile = highest cut off (25%) of data, or lowest 75% = 75th percentile
286              4 => fourth quartile (Q4) : maximal value
287
288            Example :
289
290              my @data = (1..10);
291              my $stat = Statistics::Descriptive::Full->new();
292              $stat->add_data(@data);
293              print $stat->quantile(0); # => 1
294              print $stat->quantile(1); # => 3.25
295              print $stat->quantile(2); # => 5.5
296              print $stat->quantile(3); # => 7.75
297              print $stat->quantile(4); # => 10
298
299       $stat->median();
300            Sorts the data and returns the median value of the data.
301
302       $stat->harmonic_mean();
303            Returns the harmonic mean of the data.  Since the mean is
304            undefined if any of the data are zero or if the sum of the
305            reciprocals is zero, it will return undef for both of those cases.
306
307       $stat->geometric_mean();
308            Returns the geometric mean of the data.
309
310       my $mode = $stat->mode();
311            Returns the mode of the data. The mode is the most commonly
312            occurring datum.  See
313            <http://en.wikipedia.org/wiki/Mode_%28statistics%29> . If all
314            values occur only once, then mode() will return undef.
315
316       $stat->trimmed_mean(ltrim[,utrim]);
317            "trimmed_mean(ltrim)" returns the mean with a fraction "ltrim" of
318            entries at each end dropped. "trimmed_mean(ltrim,utrim)" returns
319            the mean after a fraction "ltrim" has been removed from the lower
320            end of the data and a fraction "utrim" has been removed from the
321            upper end of the data.  This method sorts the data before
322            beginning to analyze it.
323
324            All calls to trimmed_mean() are cached so that they don't have to
325            be calculated a second time.
326
327       $stat->frequency_distribution_ref($num_partitions);
328       $stat->frequency_distribution_ref(\@bins);
329       $stat->frequency_distribution_ref();
330            "frequency_distribution_ref($num_partitions)" slices the data into
331            $num_partitions sets (where $num_partitions is greater than 1) and
332            counts the number of items that fall into each partition. It
333            returns a reference to a hash where the keys are the numerical
334            values of the partitions used. The minimum value of the data set
335            is not a key and the maximum value of the data set is always a
336            key. The number of entries for a particular partition key are the
337            number of items which are greater than the previous partition key
338            and less then or equal to the current partition key. As an
339            example,
340
341               $stat->add_data(1,1.5,2,2.5,3,3.5,4);
342               $f = $stat->frequency_distribution_ref(2);
343               for (sort {$a <=> $b} keys %$f) {
344                  print "key = $_, count = $f->{$_}\n";
345               }
346
347            prints
348
349               key = 2.5, count = 4
350               key = 4, count = 3
351
352            since there are four items less than or equal to 2.5, and 3 items
353            greater than 2.5 and less than 4.
354
355            "frequency_distribution_refs(\@bins)" provides the bins that are
356            to be used for the distribution.  This allows for non-uniform
357            distributions as well as trimmed or sample distributions to be
358            found.  @bins must be monotonic and must contain at least one
359            element.  Note that unless the set of bins contains the full range
360            of the data, the total counts returned will be less than the
361            sample size.
362
363            Calling "frequency_distribution_ref()" with no arguments returns
364            the last distribution calculated, if such exists.
365
366       my %hash = $stat->frequency_distribution($partitions);
367       my %hash = $stat->frequency_distribution(\@bins);
368       my %hash = $stat->frequency_distribution();
369            Same as "frequency_distribution_ref()" except that it returns the
370            hash clobbered into the return list. Kept for compatibility
371            reasons with previous versions of Statistics::Descriptive and
372            using it is discouraged.
373
374       $stat->least_squares_fit();
375       $stat->least_squares_fit(@x);
376            "least_squares_fit()" performs a least squares fit on the data,
377            assuming a domain of @x or a default of 1..$stat->count().  It
378            returns an array of four elements "($q, $m, $r, $rms)" where
379
380            "$q and $m"
381                satisfy the equation C($y = $m*$x + $q).
382
383            $r  is the Pearson linear correlation cofficient.
384
385            $rms
386                is the root-mean-square error.
387
388            If case of error or division by zero, the empty list is returned.
389
390            The array that is returned can be "coerced" into a hash structure
391            by doing the following:
392
393              my %hash = ();
394              @hash{'q', 'm', 'r', 'err'} = $stat->least_squares_fit();
395
396            Because calling "least_squares_fit()" with no arguments defaults
397            to using the current range, there is no caching of the results.
398

REPORTING ERRORS

400       I read my email frequently, but since adopting this module I've added 2
401       children and 1 dog to my family, so please be patient about my response
402       times.  When reporting errors, please include the following to help me
403       out:
404
405       ·   Your version of perl.  This can be obtained by typing perl "-v" at
406           the command line.
407
408       ·   Which version of Statistics::Descriptive you're using.  As you can
409           see below, I do make mistakes.  Unfortunately for me, right now
410           there are thousands of CD's with the version of this module with
411           the bugs in it.  Fortunately for you, I'm a very patient module
412           maintainer.
413
414       ·   Details about what the error is.  Try to narrow down the scope of
415           the problem and send me code that I can run to verify and track it
416           down.
417

AUTHOR

419       Current maintainer:
420
421       Shlomi Fish, <http://www.shlomifish.org/> , "shlomif@cpan.org"
422
423       Previously:
424
425       Colin Kuskie
426
427       My email address can be found at http://www.perl.com under Who's Who or
428       at: https://metacpan.org/author/COLINK .
429

CONTRIBUTORS

431       Fabio Ponciroli & Adzuna Ltd. team (outliers handling)
432

REFERENCES

434       RFC2330, Framework for IP Performance Metrics
435
436       The Art of Computer Programming, Volume 2, Donald Knuth.
437
438       Handbook of Mathematica Functions, Milton Abramowitz and Irene Stegun.
439
440       Probability and Statistics for Engineering and the Sciences, Jay
441       Devore.
442
444       Copyright (c) 1997,1998 Colin Kuskie. All rights reserved.  This
445       program is free software; you can redistribute it and/or modify it
446       under the same terms as Perl itself.
447
448       Copyright (c) 1998 Andrea Spinelli. All rights reserved.  This program
449       is free software; you can redistribute it and/or modify it under the
450       same terms as Perl itself.
451
452       Copyright (c) 1994,1995 Jason Kastner. All rights reserved.  This
453       program is free software; you can redistribute it and/or modify it
454       under the same terms as Perl itself.
455

LICENSE

457       This program is free software; you can redistribute it and/or modify it
458       under the same terms as Perl itself.
459

AUTHOR

461       Shlomi Fish <shlomif@cpan.org>
462
464       This software is copyright (c) 1997 by Jason Kastner, Andrea Spinelli,
465       Colin Kuskie, and others.
466
467       This is free software; you can redistribute it and/or modify it under
468       the same terms as the Perl 5 programming language system itself.
469

BUGS

471       Please report any bugs or feature requests on the bugtracker website
472       <https://github.com/shlomif/perl-Statistics-Descriptive/issues>
473
474       When submitting a bug or request, please include a test-file or a patch
475       to an existing test-file that illustrates the bug or desired feature.
476

SUPPORT

478   Perldoc
479       You can find documentation for this module with the perldoc command.
480
481         perldoc Statistics::Descriptive
482
483   Websites
484       The following websites have more information about this module, and may
485       be of help to you. As always, in addition to those websites please use
486       your favorite search engine to discover more resources.
487
488       ·   MetaCPAN
489
490           A modern, open-source CPAN search engine, useful to view POD in
491           HTML format.
492
493           <https://metacpan.org/release/Statistics-Descriptive>
494
495       ·   Search CPAN
496
497           The default CPAN search engine, useful to view POD in HTML format.
498
499           <http://search.cpan.org/dist/Statistics-Descriptive>
500
501       ·   RT: CPAN's Bug Tracker
502
503           The RT ( Request Tracker ) website is the default bug/issue
504           tracking system for CPAN.
505
506           <https://rt.cpan.org/Public/Dist/Display.html?Name=Statistics-Descriptive>
507
508       ·   AnnoCPAN
509
510           The AnnoCPAN is a website that allows community annotations of Perl
511           module documentation.
512
513           <http://annocpan.org/dist/Statistics-Descriptive>
514
515       ·   CPAN Ratings
516
517           The CPAN Ratings is a website that allows community ratings and
518           reviews of Perl modules.
519
520           <http://cpanratings.perl.org/d/Statistics-Descriptive>
521
522       ·   CPANTS
523
524           The CPANTS is a website that analyzes the Kwalitee ( code metrics )
525           of a distribution.
526
527           <http://cpants.cpanauthors.org/dist/Statistics-Descriptive>
528
529       ·   CPAN Testers
530
531           The CPAN Testers is a network of smoke testers who run automated
532           tests on uploaded CPAN distributions.
533
534           <http://www.cpantesters.org/distro/S/Statistics-Descriptive>
535
536       ·   CPAN Testers Matrix
537
538           The CPAN Testers Matrix is a website that provides a visual
539           overview of the test results for a distribution on various
540           Perls/platforms.
541
542           <http://matrix.cpantesters.org/?dist=Statistics-Descriptive>
543
544       ·   CPAN Testers Dependencies
545
546           The CPAN Testers Dependencies is a website that shows a chart of
547           the test results of all dependencies for a distribution.
548
549           <http://deps.cpantesters.org/?module=Statistics::Descriptive>
550
551   Bugs / Feature Requests
552       Please report any bugs or feature requests by email to
553       "bug-statistics-descriptive at rt.cpan.org", or through the web
554       interface at
555       <https://rt.cpan.org/Public/Bug/Report.html?Queue=Statistics-Descriptive>.
556       You will be automatically notified of any progress on the request by
557       the system.
558
559   Source Code
560       The code is open to the world, and available for you to hack on. Please
561       feel free to browse it and play with it, or whatever. If you want to
562       contribute patches, please send me a diff or prod me to pull from your
563       repository :)
564
565       <https://github.com/shlomif/perl-Statistics-Descriptive>
566
567         git clone git://github.com/shlomif/perl-Statistics-Descriptive.git
568
569
570
571perl v5.32.0                      2020-07-28        Statistics::Descriptive(3)
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