1Statistics::DescriptiveU:s:eSrpaCrosnet(r3i)buted Perl DSotcautmiesnttiactsi:o:nDescriptive::Sparse(3)
2
6 Statistics::Descriptive - Module of basic descriptive statistical
7 functions.
8
10 version 3.0702
11
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
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 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 Many of the methods (both Sparse and Full) cache values so that
36 subsequent calls with the same arguments are faster.
37
39 version 3.0702
40
42 Sparse Methods
43 $stat = Statistics::Descriptive::Sparse->new();
44 Create a new sparse statistics object.
45 $stat->clear();
47 Effectively the same as
48 my $class = ref($stat);
50 undef $stat;
51 $stat = new $class;
52 except more efficient.
54 $stat->add_data(1,2,3);
56 Adds data to the statistics variable. The cached statistical
57 values are updated automatically.
58 $stat->count();
60 Returns the number of data items.
61 $stat->mean();
63 Returns the mean of the data.
64 $stat->sum();
66 Returns the sum of the data.
67 $stat->variance();
69 Returns the variance of the data. Division by n-1 is used.
70 $stat->standard_deviation();
72 Returns the standard deviation of the data. Division by n-1 is
73 used.
74 $stat->min();
76 Returns the minimum value of the data set.
77 $stat->mindex();
79 Returns the index of the minimum value of the data set.
80 $stat->max();
82 Returns the maximum value of the data set.
83 $stat->maxdex();
85 Returns the index of the maximum value of the data set.
86 $stat->sample_range();
88 Returns the sample range (max - min) of the data set.
89 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 $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 $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 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 $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 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 my $value = 5;
121 my $repeat_count = 10;
122 $stat->add_data(
123 [ ($value) x $repeat_count ]
124 );
125 $stat->get_data();
127 Returns a copy of the data array.
128 $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 A function to detect outliers need to be defined (see
135 "set_outlier_filter"), otherwise the function will return an undef
136 value.
137 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 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 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 $stat->set_outlier_filter($code_ref);
152 Set the function to filter out the outlier.
153 $code_ref is the reference to the subroutine implementing the
155 filtering function.
156 Returns "undef" for invalid values of $code_ref (i.e.: not defined
158 or not a code reference), 1 otherwise.
159 · Example #1: Undefined code reference
161 my $stat = Statistics::Descriptive::Full->new();
163 $stat->add_data(1, 2, 3, 4, 5);
164 print $stat->set_outlier_filter(); # => undef
166 · Example #2: Valid code reference
168 sub outlier_filter { return $_[1] > 1; }
170 my $stat = Statistics::Descriptive::Full->new();
172 $stat->add_data( 1, 1, 1, 100, 1, );
173 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 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 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 $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 $stat->get_smoothed_data();
194 Returns a copy of the smoothed data array.
195 The smoothing method and coefficient need to be defined (see
197 "set_smoother"), otherwise the function will return an undef
198 value.
199 $stat->sort_data();
201 Sort the stored data and update the mindex and maxdex methods.
202 This method uses perl's internal sort.
203 $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 $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 $stat->kurtosis();
220 Returns the kurtosis of the data. Positive is peaked, negative is
221 flattened.
222 $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 · For example, given the 6 measurements:
229 -2, 7, 7, 4, 18, -5
231 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 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 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 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 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 (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 If the percentile method is called in a list context then it will
267 also return the index of the percentile.
268 $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 This method use the same algorithm as Excel and R language
275 (quantile type 7).
276 The generic function quantile produces sample quantiles
278 corresponding to the given probabilities.
279 $Type is an integer value between 0 to 4 :
281 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 Example :
289 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 $stat->median();
300 Sorts the data and returns the median value of the data.
301 $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 $stat->geometric_mean();
308 Returns the geometric mean of the data.
309 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 $stat->sumsq()
317 The sum of squares.
318 $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 All calls to trimmed_mean() are cached so that they don't have to
328 be calculated a second time.
329 $stat->frequency_distribution_ref($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 $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 prints
350 key = 2.5, count = 4
352 key = 4, count = 3
353 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 "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 Calling "frequency_distribution_ref()" with no arguments returns
365 the last distribution calculated, if such exists.
366 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 $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, $rms)" where
380 "$q and $m"
382 satisfy the equation C($y = $m*$x + $q).
383 $r is the Pearson linear correlation cofficient.
385 $rms
387 is the root-mean-square error.
388 If case of error or division by zero, the empty list is returned.
390 The array that is returned can be "coerced" into a hash structure
392 by doing the following:
393 my %hash = ();
395 @hash{'q', 'm', 'r', 'err'} = $stat->least_squares_fit();
396 Because calling "least_squares_fit()" with no arguments defaults
398 to using the current range, there is no caching of the results.
399
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 · Your version of perl. This can be obtained by typing perl "-v" at
407 the command line.
408 · 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 · 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
420 Current maintainer:
421 Shlomi Fish, <http://www.shlomifish.org/> , "shlomif@cpan.org"
423 Previously:
425 Colin Kuskie
427 My email address can be found at http://www.perl.com under Who's Who or
429 at: https://metacpan.org/author/COLINK .
430
432 Fabio Ponciroli & Adzuna Ltd. team (outliers handling)
433
435 RFC2330, Framework for IP Performance Metrics
436 The Art of Computer Programming, Volume 2, Donald Knuth.
438 Handbook of Mathematica Functions, Milton Abramowitz and Irene Stegun.
440 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 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 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
458 This program is free software; you can redistribute it and/or modify it
459 under the same terms as Perl itself.
460
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 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
472 Please report any bugs or feature requests on the bugtracker website
473 <https://github.com/shlomif/perl-Statistics-Descriptive/issues>
474 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
479 Perldoc
480 You can find documentation for this module with the perldoc command.
481 perldoc Statistics::Descriptive::Sparse
483 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 · MetaCPAN
490 A modern, open-source CPAN search engine, useful to view POD in
492 HTML format.
493 <https://metacpan.org/release/Statistics-Descriptive>
495 · Search CPAN
497 The default CPAN search engine, useful to view POD in HTML format.
499 <http://search.cpan.org/dist/Statistics-Descriptive>
501 · RT: CPAN's Bug Tracker
503 The RT ( Request Tracker ) website is the default bug/issue
505 tracking system for CPAN.
506 <https://rt.cpan.org/Public/Dist/Display.html?Name=Statistics-Descriptive>
508 · AnnoCPAN
510 The AnnoCPAN is a website that allows community annotations of Perl
512 module documentation.
513 <http://annocpan.org/dist/Statistics-Descriptive>
515 · CPAN Ratings
517 The CPAN Ratings is a website that allows community ratings and
519 reviews of Perl modules.
520 <http://cpanratings.perl.org/d/Statistics-Descriptive>
522 · CPANTS
524 The CPANTS is a website that analyzes the Kwalitee ( code metrics )
526 of a distribution.
527 <http://cpants.cpanauthors.org/dist/Statistics-Descriptive>
529 · CPAN Testers
531 The CPAN Testers is a network of smoke testers who run automated
533 tests on uploaded CPAN distributions.
534 <http://www.cpantesters.org/distro/S/Statistics-Descriptive>
536 · CPAN Testers Matrix
538 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 <http://matrix.cpantesters.org/?dist=Statistics-Descriptive>
544 · CPAN Testers Dependencies
546 The CPAN Testers Dependencies is a website that shows a chart of
548 the test results of all dependencies for a distribution.
549 <http://deps.cpantesters.org/?module=Statistics::Descriptive>
551 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 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 <https://github.com/shlomif/perl-Statistics-Descriptive>
567 git clone git://github.com/shlomif/perl-Statistics-Descriptive.git
569perl v5.32.0 2020-07-28Statistics::Descriptive::Sparse(3)