1Statistics::DescriptiveU:s:eSrpaCrosnet(r3i)buted Perl DSotcautmiesnttiactsi:o:nDescriptive::Sparse(3)
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3
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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->sumsq()
317            The sum of squares.
318
319       $stat->trimmed_mean(ltrim[,utrim]);
320            "trimmed_mean(ltrim)" returns the mean with a fraction "ltrim" of
321            entries at each end dropped. "trimmed_mean(ltrim,utrim)" returns
322            the mean after a fraction "ltrim" has been removed from the lower
323            end of the data and a fraction "utrim" has been removed from the
324            upper end of the data.  This method sorts the data before
325            beginning to analyze it.
326
327            All calls to trimmed_mean() are cached so that they don't have to
328            be calculated a second time.
329
330       $stat->frequency_distribution_ref($partitions);
331       $stat->frequency_distribution_ref(\@bins);
332       $stat->frequency_distribution_ref();
333            "frequency_distribution_ref($partitions)" slices the data into
334            $partition sets (where $partition is greater than 1) and counts
335            the number of items that fall into each partition. It returns a
336            reference to a hash where the keys are the numerical values of the
337            partitions used. The minimum value of the data set is not a key
338            and the maximum value of the data set is always a key. The number
339            of entries for a particular partition key are the number of items
340            which are greater than the previous partition key and less then or
341            equal to the current partition key. As an example,
342
343               $stat->add_data(1,1.5,2,2.5,3,3.5,4);
344               $f = $stat->frequency_distribution_ref(2);
345               for (sort {$a <=> $b} keys %$f) {
346                  print "key = $_, count = $f->{$_}\n";
347               }
348
349            prints
350
351               key = 2.5, count = 4
352               key = 4, count = 3
353
354            since there are four items less than or equal to 2.5, and 3 items
355            greater than 2.5 and less than 4.
356
357            "frequency_distribution_refs(\@bins)" provides the bins that are
358            to be used for the distribution.  This allows for non-uniform
359            distributions as well as trimmed or sample distributions to be
360            found.  @bins must be monotonic and contain at least one element.
361            Note that unless the set of bins contains the range that the total
362            counts returned will be less than the sample size.
363
364            Calling "frequency_distribution_ref()" with no arguments returns
365            the last distribution calculated, if such exists.
366
367       my %hash = $stat->frequency_distribution($partitions);
368       my %hash = $stat->frequency_distribution(\@bins);
369       my %hash = $stat->frequency_distribution();
370            Same as "frequency_distribution_ref()" except that returns the
371            hash clobbered into the return list. Kept for compatibility
372            reasons with previous versions of Statistics::Descriptive and
373            using it is discouraged.
374
375       $stat->least_squares_fit();
376       $stat->least_squares_fit(@x);
377            "least_squares_fit()" performs a least squares fit on the data,
378            assuming a domain of @x or a default of 1..$stat->count().  It
379            returns an array of four elements "($q, $m, $r, $rms)" where
380
381            "$q and $m"
382                satisfy the equation C($y = $m*$x + $q).
383
384            $r  is the Pearson linear correlation cofficient.
385
386            $rms
387                is the root-mean-square error.
388
389            If case of error or division by zero, the empty list is returned.
390
391            The array that is returned can be "coerced" into a hash structure
392            by doing the following:
393
394              my %hash = ();
395              @hash{'q', 'm', 'r', 'err'} = $stat->least_squares_fit();
396
397            Because calling "least_squares_fit()" with no arguments defaults
398            to using the current range, there is no caching of the results.
399

REPORTING ERRORS

401       I read my email frequently, but since adopting this module I've added 2
402       children and 1 dog to my family, so please be patient about my response
403       times.  When reporting errors, please include the following to help me
404       out:
405
406       ·   Your version of perl.  This can be obtained by typing perl "-v" at
407           the command line.
408
409       ·   Which version of Statistics::Descriptive you're using.  As you can
410           see below, I do make mistakes.  Unfortunately for me, right now
411           there are thousands of CD's with the version of this module with
412           the bugs in it.  Fortunately for you, I'm a very patient module
413           maintainer.
414
415       ·   Details about what the error is.  Try to narrow down the scope of
416           the problem and send me code that I can run to verify and track it
417           down.
418

AUTHOR

420       Current maintainer:
421
422       Shlomi Fish, <http://www.shlomifish.org/> , "shlomif@cpan.org"
423
424       Previously:
425
426       Colin Kuskie
427
428       My email address can be found at http://www.perl.com under Who's Who or
429       at: https://metacpan.org/author/COLINK .
430

CONTRIBUTORS

432       Fabio Ponciroli & Adzuna Ltd. team (outliers handling)
433

REFERENCES

435       RFC2330, Framework for IP Performance Metrics
436
437       The Art of Computer Programming, Volume 2, Donald Knuth.
438
439       Handbook of Mathematica Functions, Milton Abramowitz and Irene Stegun.
440
441       Probability and Statistics for Engineering and the Sciences, Jay
442       Devore.
443
445       Copyright (c) 1997,1998 Colin Kuskie. All rights reserved.  This
446       program is free software; you can redistribute it and/or modify it
447       under the same terms as Perl itself.
448
449       Copyright (c) 1998 Andrea Spinelli. All rights reserved.  This program
450       is free software; you can redistribute it and/or modify it under the
451       same terms as Perl itself.
452
453       Copyright (c) 1994,1995 Jason Kastner. All rights reserved.  This
454       program is free software; you can redistribute it and/or modify it
455       under the same terms as Perl itself.
456

LICENSE

458       This program is free software; you can redistribute it and/or modify it
459       under the same terms as Perl itself.
460

AUTHOR

462       Shlomi Fish <shlomif@cpan.org>
463
465       This software is copyright (c) 1997 by Jason Kastner, Andrea Spinelli,
466       Colin Kuskie, and others.
467
468       This is free software; you can redistribute it and/or modify it under
469       the same terms as the Perl 5 programming language system itself.
470

BUGS

472       Please report any bugs or feature requests on the bugtracker website
473       <https://github.com/shlomif/perl-Statistics-Descriptive/issues>
474
475       When submitting a bug or request, please include a test-file or a patch
476       to an existing test-file that illustrates the bug or desired feature.
477

SUPPORT

479   Perldoc
480       You can find documentation for this module with the perldoc command.
481
482         perldoc Statistics::Descriptive::Sparse
483
484   Websites
485       The following websites have more information about this module, and may
486       be of help to you. As always, in addition to those websites please use
487       your favorite search engine to discover more resources.
488
489       ·   MetaCPAN
490
491           A modern, open-source CPAN search engine, useful to view POD in
492           HTML format.
493
494           <https://metacpan.org/release/Statistics-Descriptive>
495
496       ·   Search CPAN
497
498           The default CPAN search engine, useful to view POD in HTML format.
499
500           <http://search.cpan.org/dist/Statistics-Descriptive>
501
502       ·   RT: CPAN's Bug Tracker
503
504           The RT ( Request Tracker ) website is the default bug/issue
505           tracking system for CPAN.
506
507           <https://rt.cpan.org/Public/Dist/Display.html?Name=Statistics-Descriptive>
508
509       ·   AnnoCPAN
510
511           The AnnoCPAN is a website that allows community annotations of Perl
512           module documentation.
513
514           <http://annocpan.org/dist/Statistics-Descriptive>
515
516       ·   CPAN Ratings
517
518           The CPAN Ratings is a website that allows community ratings and
519           reviews of Perl modules.
520
521           <http://cpanratings.perl.org/d/Statistics-Descriptive>
522
523       ·   CPANTS
524
525           The CPANTS is a website that analyzes the Kwalitee ( code metrics )
526           of a distribution.
527
528           <http://cpants.cpanauthors.org/dist/Statistics-Descriptive>
529
530       ·   CPAN Testers
531
532           The CPAN Testers is a network of smoke testers who run automated
533           tests on uploaded CPAN distributions.
534
535           <http://www.cpantesters.org/distro/S/Statistics-Descriptive>
536
537       ·   CPAN Testers Matrix
538
539           The CPAN Testers Matrix is a website that provides a visual
540           overview of the test results for a distribution on various
541           Perls/platforms.
542
543           <http://matrix.cpantesters.org/?dist=Statistics-Descriptive>
544
545       ·   CPAN Testers Dependencies
546
547           The CPAN Testers Dependencies is a website that shows a chart of
548           the test results of all dependencies for a distribution.
549
550           <http://deps.cpantesters.org/?module=Statistics::Descriptive>
551
552   Bugs / Feature Requests
553       Please report any bugs or feature requests by email to
554       "bug-statistics-descriptive at rt.cpan.org", or through the web
555       interface at
556       <https://rt.cpan.org/Public/Bug/Report.html?Queue=Statistics-Descriptive>.
557       You will be automatically notified of any progress on the request by
558       the system.
559
560   Source Code
561       The code is open to the world, and available for you to hack on. Please
562       feel free to browse it and play with it, or whatever. If you want to
563       contribute patches, please send me a diff or prod me to pull from your
564       repository :)
565
566       <https://github.com/shlomif/perl-Statistics-Descriptive>
567
568         git clone git://github.com/shlomif/perl-Statistics-Descriptive.git
569
570
571
572perl v5.32.0                      2020-07-28Statistics::Descriptive::Sparse(3)
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