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 Cached values from Full methods are deleted since they are no longer valid.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->add_data_with_samples([{1 => 10}, {2 => 20}, {3 => 30},]);

Add data to the statistics variable and set the number of samples each value has been built with. The data is the key of each element of the input array ref, while the value is the number of samples: [{data1 => smaples1}, {data2 => samples2}, ...].

NOTE: The number of samples is only used by the smoothing function and is ignored otherwise. It is not equivalent to repeat count. In order to repeat a certain datum more than one time call add_data() like this:

    my $value = 5;
    my $repeat_count = 10;
    $stat->add_data(
        [ ($value) x $repeat_count ]
    );
    

$stat->get_data();

Returns a copy of the data array.

$stat->get_data_without_outliers();

Returns a copy of the data array without outliers. The number minimum of samples to apply the outlier filtering is $Statistics::Descriptive::Min_samples_number, 4 by default.

A function to detect outliers need to be defined (see "set_outlier_filter"), otherwise the function will return an undef value.

The filtering will act only on the most extreme value of the data set (i.e.: value with the highest absolute standard deviation from the mean).

If there is the need to remove more than one outlier, the filtering need to be re-run for the next most extreme value with the initial outlier removed.

This is not always needed since the test (for example Grubb's test) usually can only detect the most exreme value. If there is more than one extreme case in a set, then the standard deviation will be high enough to make neither case an outlier.

$stat->set_outlier_filter($code_ref);

Set the function to filter out the outlier.

$code_ref is the reference to the subroutine implementing the filtering function.

Returns "undef" for invalid values of $code_ref (i.e.: not defined or not a code reference), 1 otherwise.

$stat->set_smoother({ method => 'exponential', coeff => 0, });

Set the method used to smooth the data and the smoothing coefficient. See "Statistics::Descriptive::Smoother" for more details.

$stat->get_smoothed_data();

Returns a copy of the smoothed data array.

The smoothing method and coefficient need to be defined (see "set_smoother"), otherwise the function will return an undef value.

$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.

$stat->skewness();

Returns the skewness of the data. A value of zero is no skew, negative is a left skewed tail, positive is a right skewed tail. This is consistent with Excel.

$stat->kurtosis();

Returns the kurtosis of the data. Positive is peaked, negative is flattened.

$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:

$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
    

Example :

  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.

my $mode = $stat->mode();

Returns the mode of the data. The mode is the most commonly occurring datum. See <http://en.wikipedia.org/wiki/Mode_%28statistics%29> . If all values occur only once, then mode() will return undef.

$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.

$stat->frequency_distribution_ref($num_partitions);

$stat->frequency_distribution_ref(\@bins);

$stat->frequency_distribution_ref();

"frequency_distribution_ref($num_partitions)" slices the data into $num_partitions sets (where $num_partitions 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 must contain at least one element. Note that unless the set of bins contains the full range of the data, 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 it 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

  my %hash = ();
  @hash{'q', 'm', 'r', 'err'} = $stat->least_squares_fit();

Websites¶

The following websites have more information about this module, and may be of help to you. As always, in addition to those websites please use your favorite search engine to discover more resources.

• MetaCPAN

  A modern, open-source CPAN search engine, useful to view POD in HTML format.

  <https://metacpan.org/release/Statistics-Descriptive>

• RT: CPAN's Bug Tracker

  The RT ( Request Tracker ) website is the default bug/issue tracking system for CPAN.

  <https://rt.cpan.org/Public/Dist/Display.html?Name=Statistics-Descriptive>

• CPANTS

  The CPANTS is a website that analyzes the Kwalitee ( code metrics ) of a distribution.

  <http://cpants.cpanauthors.org/dist/Statistics-Descriptive>

• CPAN Testers

  The CPAN Testers is a network of smoke testers who run automated tests on uploaded CPAN distributions.

  <http://www.cpantesters.org/distro/S/Statistics-Descriptive>

• CPAN Testers Matrix

  The CPAN Testers Matrix is a website that provides a visual overview of the test results for a distribution on various Perls/platforms.

  <http://matrix.cpantesters.org/?dist=Statistics-Descriptive>

• CPAN Testers Dependencies

  The CPAN Testers Dependencies is a website that shows a chart of the test results of all dependencies for a distribution.

  <http://deps.cpantesters.org/?module=Statistics::Descriptive>

Bugs / Feature Requests¶

Please report any bugs or feature requests by email to "bug-statistics-descriptive at rt.cpan.org", or through the web interface at <https://rt.cpan.org/Public/Bug/Report.html?Queue=Statistics-Descriptive>. You will be automatically notified of any progress on the request by the system.

Source Code¶

The code is open to the world, and available for you to hack on. Please feel free to browse it and play with it, or whatever. If you want to contribute patches, please send me a diff or prod me to pull from your repository :)

<https://github.com/shlomif/perl-Statistics-Descriptive>

  git clone git://github.com/shlomif/perl-Statistics-Descriptive.git