SparseMethods
$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.
FullMethods
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Cached values from Full methods are deleted since they are no longer valid.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:Callingadd_datawithanemptyarraywilldeleteallofyourFullmethodcachedvalues!Cachedvaluesforthesparsemethodsarenotchanged
$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.
• Example #1: Undefined code reference
my $stat = Statistics::Descriptive::Full->new();
$stat->add_data(1, 2, 3, 4, 5);
print $stat->set_outlier_filter(); # => undef
• Example #2: Valid code reference
sub outlier_filter { return $_[1] > 1; }
my $stat = Statistics::Descriptive::Full->new();
$stat->add_data( 1, 1, 1, 100, 1, );
print $stat->set_outlier_filter( \&outlier_filter ); # => 1
my @filtered_data = $stat->get_data_without_outliers();
# @filtered_data is (1, 1, 1, 1)
In this example the series is really simple and the outlier filter function as well. For more
complex series the outlier filter function might be more complex (see Grubbs' test for
outliers).
The outlier filter function will receive as first parameter the Statistics::Descriptive::Full
object, as second the value of the candidate outlier. Having the object in the function might be
useful for complex filters where statistics property are needed (again see Grubbs' test for
outlier).
$stat->set_smoother({ method => 'exponential', coeff => 0, });
Set the method used to smooth the data and the smoothing coefficient. See "Statistics::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:
• For example, given the 6 measurements:
-2, 7, 7, 4, 18, -5
Then F(-8) = 0, F(-5) = 1/6, F(-5.0001) = 0, F(-4.999) = 1/6, F(7) = 5/6, F(18) = 1, F(239) = 1.
Note that we can recover the different measured values and how many times each occurred from
F(x) -- no information regarding the range in values is lost. Summarizing measurements using
histograms, on the other hand, in general loses information about the different values observed,
so the EDF is preferred.
Using either the EDF or a histogram, however, we do lose information regarding the order in
which the values were observed. Whether this loss is potentially significant will depend on the
metric being measured.
We will use the term "percentile" to refer to the smallest value of x for which F(x) >= a given
percentage. So the 50th percentile of the example above is 4, since F(4) = 3/6 = 50%; the 25th
percentile is -2, since F(-5) = 1/6 < 25%, and F(-2) = 2/6 >= 25%; the 100th percentile is 18;
and the 0th percentile is -infinity, as is the 15th percentile, which for ease of handling and
backward compatibility is returned as undef() by the function.
Care must be taken when using percentiles to summarize a sample, because they can lend an
unwarranted appearance of more precision than is really available. Any such summary must
include the sample size N, because any percentile difference finer than 1/N is below the
resolution of the sample.
(Taken from: RFC2330-FrameworkforIPPerformanceMetrics, Section 11.3. Defining Statistical
Distributions. RFC2330 is available from: <http://www.ietf.org/rfc/rfc2330.txt> .)
If the percentile method is called in a list context then it will also return the index of the
percentile.
$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 type7).
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->sumsq()
The sum of squares.
$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.
$stat->frequency_distribution_ref($partitions);
$stat->frequency_distribution_ref(\@bins);
$stat->frequency_distribution_ref();
"frequency_distribution_ref($partitions)" slices the data into $partition sets (where $partition 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 contain at least one element. Note that unless the set of bins contains
the range that 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 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, $rms)" where
"$q and $m"
satisfy the equation C($y = $m*$x + $q).
$r is the Pearson linear correlation cofficient.
$rms
is the root-mean-square error.
If case of error or division by zero, the empty list is returned.
The array that is returned can be "coerced" into a hash structure by doing the following:
my %hash = ();
@hash{'q', 'm', 'r', 'err'} = $stat->least_squares_fit();
Because calling "least_squares_fit()" with no arguments defaults to using the current range, there
is no caching of the results.
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