1Statistics::DescriptiveU(s3eprm)Contributed Perl DocumenSttaattiiosntics::Descriptive(3pm)
2
6 Statistics::Descriptive - Module of basic descriptive statistical
7 functions.
8
10 version 3.0801
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 Sparse Methods
40 $stat = Statistics::Descriptive::Sparse->new();
41 Create a new sparse statistics object.
42 $stat->clear();
44 Effectively the same as
45 my $class = ref($stat);
47 undef $stat;
48 $stat = new $class;
49 except more efficient.
51 $stat->add_data(1,2,3);
53 Adds data to the statistics variable. The cached statistical
54 values are updated automatically.
55 $stat->count();
57 Returns the number of data items.
58 $stat->mean();
60 Returns the mean of the data.
61 $stat->sum();
63 Returns the sum of the data.
64 $stat->variance();
66 Returns the variance of the data. Division by n-1 is used.
67 $stat->standard_deviation();
69 Returns the standard deviation of the data. Division by n-1 is
70 used.
71 $stat->min();
73 Returns the minimum value of the data set.
74 $stat->mindex();
76 Returns the index of the minimum value of the data set.
77 $stat->max();
79 Returns the maximum value of the data set.
80 $stat->maxdex();
82 Returns the index of the maximum value of the data set.
83 $stat->sample_range();
85 Returns the sample range (max - min) of the data set.
86 Full Methods
88 Similar to the Sparse Methods above, any Full Method that is called
89 caches the current result so that it doesn't have to be recalculated.
90 In some cases, several values can be cached at the same time.
91 $stat = Statistics::Descriptive::Full->new();
93 Create a new statistics object that inherits from
94 Statistics::Descriptive::Sparse so that it contains all the
95 methods described above.
96 $stat->add_data(1,2,4,5);
98 Adds data to the statistics variable. All of the sparse
99 statistical values are updated and cached. Cached values from
100 Full methods are deleted since they are no longer valid.
101 Note: Calling add_data with an empty array will delete all of
103 your Full method cached values! Cached values for the sparse
104 methods are not changed
105 $stat->add_data_with_samples([{1 => 10}, {2 => 20}, {3 => 30},]);
107 Add data to the statistics variable and set the number of samples
108 each value has been built with. The data is the key of each
109 element of the input array ref, while the value is the number of
110 samples: [{data1 => smaples1}, {data2 => samples2}, ...].
111 NOTE: The number of samples is only used by the smoothing function
113 and is ignored otherwise. It is not equivalent to repeat count. In
114 order to repeat a certain datum more than one time call add_data()
115 like this:
116 my $value = 5;
118 my $repeat_count = 10;
119 $stat->add_data(
120 [ ($value) x $repeat_count ]
121 );
122 $stat->get_data();
124 Returns a copy of the data array.
125 $stat->get_data_without_outliers();
127 Returns a copy of the data array without outliers. The number
128 minimum of samples to apply the outlier filtering is
129 $Statistics::Descriptive::Min_samples_number, 4 by default.
130 A function to detect outliers need to be defined (see
132 "set_outlier_filter"), otherwise the function will return an undef
133 value.
134 The filtering will act only on the most extreme value of the data
136 set (i.e.: value with the highest absolute standard deviation from
137 the mean).
138 If there is the need to remove more than one outlier, the
140 filtering need to be re-run for the next most extreme value with
141 the initial outlier removed.
142 This is not always needed since the test (for example Grubb's
144 test) usually can only detect the most exreme value. If there is
145 more than one extreme case in a set, then the standard deviation
146 will be high enough to make neither case an outlier.
147 $stat->set_outlier_filter($code_ref);
149 Set the function to filter out the outlier.
150 $code_ref is the reference to the subroutine implementing the
152 filtering function.
153 Returns "undef" for invalid values of $code_ref (i.e.: not defined
155 or not a code reference), 1 otherwise.
156 • Example #1: Undefined code reference
158 my $stat = Statistics::Descriptive::Full->new();
160 $stat->add_data(1, 2, 3, 4, 5);
161 print $stat->set_outlier_filter(); # => undef
163 • Example #2: Valid code reference
165 sub outlier_filter { return $_[1] > 1; }
167 my $stat = Statistics::Descriptive::Full->new();
169 $stat->add_data( 1, 1, 1, 100, 1, );
170 print $stat->set_outlier_filter( \&outlier_filter ); # => 1
172 my @filtered_data = $stat->get_data_without_outliers();
173 # @filtered_data is (1, 1, 1, 1)
174 In this example the series is really simple and the outlier
176 filter function as well. For more complex series the outlier
177 filter function might be more complex (see Grubbs' test for
178 outliers).
179 The outlier filter function will receive as first parameter
181 the Statistics::Descriptive::Full object, as second the value
182 of the candidate outlier. Having the object in the function
183 might be useful for complex filters where statistics property
184 are needed (again see Grubbs' test for outlier).
185 $stat->set_smoother({ method => 'exponential', coeff => 0, });
187 Set the method used to smooth the data and the smoothing
188 coefficient. See "Statistics::Descriptive::Smoother" for more
189 details.
190 $stat->get_smoothed_data();
192 Returns a copy of the smoothed data array.
193 The smoothing method and coefficient need to be defined (see
195 "set_smoother"), otherwise the function will return an undef
196 value.
197 $stat->sort_data();
199 Sort the stored data and update the mindex and maxdex methods.
200 This method uses perl's internal sort.
201 $stat->presorted(1);
203 $stat->presorted();
204 If called with a non-zero argument, this method sets a flag that
205 says the data is already sorted and need not be sorted again.
206 Since some of the methods in this class require sorted data, this
207 saves some time. If you supply sorted data to the object, call
208 this method to prevent the data from being sorted again. The flag
209 is cleared whenever add_data is called. Calling the method
210 without an argument returns the value of the flag.
211 $stat->skewness();
213 Returns the skewness of the data. A value of zero is no skew,
214 negative is a left skewed tail, positive is a right skewed tail.
215 This is consistent with Excel.
216 $stat->kurtosis();
218 Returns the kurtosis of the data. Positive is peaked, negative is
219 flattened.
220 $x = $stat->percentile(25);
222 ($x, $index) = $stat->percentile(25);
223 Sorts the data and returns the value that corresponds to the
224 percentile as defined in RFC2330:
225 • For example, given the 6 measurements:
227 -2, 7, 7, 4, 18, -5
229 Then F(-8) = 0, F(-5) = 1/6, F(-5.0001) = 0, F(-4.999) = 1/6,
231 F(7) = 5/6, F(18) = 1, F(239) = 1.
232 Note that we can recover the different measured values and how
234 many times each occurred from F(x) -- no information regarding
235 the range in values is lost. Summarizing measurements using
236 histograms, on the other hand, in general loses information
237 about the different values observed, so the EDF is preferred.
238 Using either the EDF or a histogram, however, we do lose
240 information regarding the order in which the values were
241 observed. Whether this loss is potentially significant will
242 depend on the metric being measured.
243 We will use the term "percentile" to refer to the smallest
245 value of x for which F(x) >= a given percentage. So the 50th
246 percentile of the example above is 4, since F(4) = 3/6 = 50%;
247 the 25th percentile is -2, since F(-5) = 1/6 < 25%, and F(-2)
248 = 2/6 >= 25%; the 100th percentile is 18; and the 0th
249 percentile is -infinity, as is the 15th percentile, which for
250 ease of handling and backward compatibility is returned as
251 undef() by the function.
252 Care must be taken when using percentiles to summarize a
254 sample, because they can lend an unwarranted appearance of
255 more precision than is really available. Any such summary
256 must include the sample size N, because any percentile
257 difference finer than 1/N is below the resolution of the
258 sample.
259 (Taken from: RFC2330 - Framework for IP Performance Metrics,
261 Section 11.3. Defining Statistical Distributions. RFC2330 is
262 available from: <http://www.ietf.org/rfc/rfc2330.txt> .)
263 If the percentile method is called in a list context then it will
265 also return the index of the percentile.
266 $x = $stat->quantile($Type);
268 Sorts the data and returns estimates of underlying distribution
269 quantiles based on one or two order statistics from the supplied
270 elements.
271 This method use the same algorithm as Excel and R language
273 (quantile type 7).
274 The generic function quantile produces sample quantiles
276 corresponding to the given probabilities.
277 $Type is an integer value between 0 to 4 :
279 0 => zero quartile (Q0) : minimal value
281 1 => first quartile (Q1) : lower quartile = lowest cut off (25%) of data = 25th percentile
282 2 => second quartile (Q2) : median = it cuts data set in half = 50th percentile
283 3 => third quartile (Q3) : upper quartile = highest cut off (25%) of data, or lowest 75% = 75th percentile
284 4 => fourth quartile (Q4) : maximal value
285 Example :
287 my @data = (1..10);
289 my $stat = Statistics::Descriptive::Full->new();
290 $stat->add_data(@data);
291 print $stat->quantile(0); # => 1
292 print $stat->quantile(1); # => 3.25
293 print $stat->quantile(2); # => 5.5
294 print $stat->quantile(3); # => 7.75
295 print $stat->quantile(4); # => 10
296 $stat->median();
298 Sorts the data and returns the median value of the data.
299 $stat->harmonic_mean();
301 Returns the harmonic mean of the data. Since the mean is
302 undefined if any of the data are zero or if the sum of the
303 reciprocals is zero, it will return undef for both of those cases.
304 $stat->geometric_mean();
306 Returns the geometric mean of the data.
307 my $mode = $stat->mode();
309 Returns the mode of the data. The mode is the most commonly
310 occurring datum. See
311 <http://en.wikipedia.org/wiki/Mode_%28statistics%29> . If all
312 values occur only once, then mode() will return undef.
313 $stat->trimmed_mean(ltrim[,utrim]);
315 trimmed_mean(ltrim) returns the mean with a fraction "ltrim" of
316 entries at each end dropped. "trimmed_mean(ltrim,utrim)" returns
317 the mean after a fraction "ltrim" has been removed from the lower
318 end of the data and a fraction "utrim" has been removed from the
319 upper end of the data. This method sorts the data before
320 beginning to analyze it.
321 All calls to trimmed_mean() are cached so that they don't have to
323 be calculated a second time.
324 $stat->frequency_distribution_ref($num_partitions);
326 $stat->frequency_distribution_ref(\@bins);
327 $stat->frequency_distribution_ref();
328 frequency_distribution_ref($num_partitions) slices the data into
329 $num_partitions sets (where $num_partitions is greater than 1) and
330 counts the number of items that fall into each partition. It
331 returns a reference to a hash where the keys are the numerical
332 values of the partitions used. The minimum value of the data set
333 is not a key and the maximum value of the data set is always a
334 key. The number of entries for a particular partition key are the
335 number of items which are greater than the previous partition key
336 and less then or equal to the current partition key. As an
337 example,
338 $stat->add_data(1,1.5,2,2.5,3,3.5,4);
340 $f = $stat->frequency_distribution_ref(2);
341 for (sort {$a <=> $b} keys %$f) {
342 print "key = $_, count = $f->{$_}\n";
343 }
344 prints
346 key = 2.5, count = 4
348 key = 4, count = 3
349 since there are four items less than or equal to 2.5, and 3 items
351 greater than 2.5 and less than 4.
352 frequency_distribution_refs(\@bins) provides the bins that are to
354 be used for the distribution. This allows for non-uniform
355 distributions as well as trimmed or sample distributions to be
356 found. @bins must be monotonic and must contain at least one
357 element. Note that unless the set of bins contains the full range
358 of the data, the total counts returned will be less than the
359 sample size.
360 Calling frequency_distribution_ref() with no arguments returns the
362 last distribution calculated, if such exists.
363 my %hash = $stat->frequency_distribution($partitions);
365 my %hash = $stat->frequency_distribution(\@bins);
366 my %hash = $stat->frequency_distribution();
367 Same as frequency_distribution_ref() except that it returns the
368 hash clobbered into the return list. Kept for compatibility
369 reasons with previous versions of Statistics::Descriptive and
370 using it is discouraged.
371 $stat->least_squares_fit();
373 $stat->least_squares_fit(@x);
374 least_squares_fit() performs a least squares fit on the data,
375 assuming a domain of @x or a default of 1..$stat->count(). It
376 returns an array of four elements "($q, $m, $r, $rms)" where
377 "$q and $m"
379 satisfy the equation C($y = $m*$x + $q).
380 $r is the Pearson linear correlation cofficient.
382 $rms
384 is the root-mean-square error.
385 If case of error or division by zero, the empty list is returned.
387 The array that is returned can be "coerced" into a hash structure
389 by doing the following:
390 my %hash = ();
392 @hash{'q', 'm', 'r', 'err'} = $stat->least_squares_fit();
393 Because calling least_squares_fit() with no arguments defaults to
395 using the current range, there is no caching of the results.
396
398 I read my email frequently, but since adopting this module I've added 2
399 children and 1 dog to my family, so please be patient about my response
400 times. When reporting errors, please include the following to help me
401 out:
402 • Your version of perl. This can be obtained by typing perl "-v" at
404 the command line.
405 • Which version of Statistics::Descriptive you're using. As you can
407 see below, I do make mistakes. Unfortunately for me, right now
408 there are thousands of CD's with the version of this module with
409 the bugs in it. Fortunately for you, I'm a very patient module
410 maintainer.
411 • Details about what the error is. Try to narrow down the scope of
413 the problem and send me code that I can run to verify and track it
414 down.
415
417 Current maintainer:
418 Shlomi Fish, <http://www.shlomifish.org/> , "shlomif@cpan.org"
420 Previously:
422 Colin Kuskie
424 My email address can be found at http://www.perl.com under Who's Who or
426 at: https://metacpan.org/author/COLINK .
427
429 Fabio Ponciroli & Adzuna Ltd. team (outliers handling)
430
432 RFC2330, Framework for IP Performance Metrics
433 The Art of Computer Programming, Volume 2, Donald Knuth.
435 Handbook of Mathematica Functions, Milton Abramowitz and Irene Stegun.
437 Probability and Statistics for Engineering and the Sciences, Jay
439 Devore.
440
442 Copyright (c) 1997,1998 Colin Kuskie. All rights reserved. This
443 program is free software; you can redistribute it and/or modify it
444 under the same terms as Perl itself.
445 Copyright (c) 1998 Andrea Spinelli. All rights reserved. This program
447 is free software; you can redistribute it and/or modify it under the
448 same terms as Perl itself.
449 Copyright (c) 1994,1995 Jason Kastner. All rights reserved. This
451 program is free software; you can redistribute it and/or modify it
452 under the same terms as Perl itself.
453
455 This program is free software; you can redistribute it and/or modify it
456 under the same terms as Perl itself.
457
459 Websites
460 The following websites have more information about this module, and may
461 be of help to you. As always, in addition to those websites please use
462 your favorite search engine to discover more resources.
463 • MetaCPAN
465 A modern, open-source CPAN search engine, useful to view POD in
467 HTML format.
468 <https://metacpan.org/release/Statistics-Descriptive>
470 • RT: CPAN's Bug Tracker
472 The RT ( Request Tracker ) website is the default bug/issue
474 tracking system for CPAN.
475 <https://rt.cpan.org/Public/Dist/Display.html?Name=Statistics-Descriptive>
477 • CPANTS
479 The CPANTS is a website that analyzes the Kwalitee ( code metrics )
481 of a distribution.
482 <http://cpants.cpanauthors.org/dist/Statistics-Descriptive>
484 • CPAN Testers
486 The CPAN Testers is a network of smoke testers who run automated
488 tests on uploaded CPAN distributions.
489 <http://www.cpantesters.org/distro/S/Statistics-Descriptive>
491 • CPAN Testers Matrix
493 The CPAN Testers Matrix is a website that provides a visual
495 overview of the test results for a distribution on various
496 Perls/platforms.
497 <http://matrix.cpantesters.org/?dist=Statistics-Descriptive>
499 • CPAN Testers Dependencies
501 The CPAN Testers Dependencies is a website that shows a chart of
503 the test results of all dependencies for a distribution.
504 <http://deps.cpantesters.org/?module=Statistics::Descriptive>
506 Bugs / Feature Requests
508 Please report any bugs or feature requests by email to
509 "bug-statistics-descriptive at rt.cpan.org", or through the web
510 interface at
511 <https://rt.cpan.org/Public/Bug/Report.html?Queue=Statistics-Descriptive>.
512 You will be automatically notified of any progress on the request by
513 the system.
514 Source Code
516 The code is open to the world, and available for you to hack on. Please
517 feel free to browse it and play with it, or whatever. If you want to
518 contribute patches, please send me a diff or prod me to pull from your
519 repository :)
520 <https://github.com/shlomif/perl-Statistics-Descriptive>
522 git clone git://github.com/shlomif/perl-Statistics-Descriptive.git
524
526 Shlomi Fish <shlomif@cpan.org>
527
529 Please report any bugs or feature requests on the bugtracker website
530 <https://github.com/shlomif/perl-Statistics-Descriptive/issues>
531 When submitting a bug or request, please include a test-file or a patch
533 to an existing test-file that illustrates the bug or desired feature.
534
536 This software is copyright (c) 1997 by Jason Kastner, Andrea Spinelli,
537 Colin Kuskie, and others.
538 This is free software; you can redistribute it and/or modify it under
540 the same terms as the Perl 5 programming language system itself.
541perl v5.38.0 2023-07-21 Statistics::Descriptive(3pm)