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# NAME

Statistics::Descriptive::Discrete - Compute descriptive statistics for discrete data sets.

To install, use the CPAN module (https://metacpan.org/pod/Statistics::Descriptive::Discrete).

# SYNOPSIS

``````  use Statistics::Descriptive::Discrete;

my \$stats = new Statistics::Descriptive::Discrete;
print "count = ",\$stats->count(),"\n";
print "uniq  = ",\$stats->uniq(),"\n";
print "sum = ",\$stats->sum(),"\n";
print "min = ",\$stats->min(),"\n";
print "min index = ",\$stats->mindex(),"\n";
print "max = ",\$stats->max(),"\n";
print "max index = ",\$stats->maxdex(),"\n";
print "mean = ",\$stats->mean(),"\n";
print "geometric mean = ",\$stats->geometric_mean(),"\n";
print "harmonic mean = ", \$stats->harmonic_mean(),"\n";
print "standard_deviation = ",\$stats->standard_deviation(),"\n";
print "variance = ",\$stats->variance(),"\n";
print "sample_range = ",\$stats->sample_range(),"\n";
print "mode = ",\$stats->mode(),"\n";
print "median = ",\$stats->median(),"\n";
my \$f = \$stats->frequency_distribution_ref(3);
for (sort {\$a <=> \$b} keys %\$f) {
print "key = \$_, count = \$f->{\$_}\n";
}``````

# DESCRIPTION

This module provides basic functions used in descriptive statistics. It borrows very heavily from Statistics::Descriptive::Full (which is included with Statistics::Descriptive) with one major difference. This module is optimized for discretized data e.g. data from an A/D conversion that has a discrete set of possible values. E.g. if your data is produced by an 8 bit A/D then you'd have only 256 possible values in your data set. Even though you might have a million data points, you'd only have 256 different values in those million points. Instead of storing the entire data set as Statistics::Descriptive does, this module only stores the values seen and the number of times each value occurs.

For very large data sets, this storage method results in significant speed and memory improvements. For example, for an 8-bit data set (256 possible values), with 1,000,000 data points, this module is about 10x faster than Statistics::Descriptive::Full or Statistics::Descriptive::Sparse.

Statistics::Descriptive run time is a factor of the size of the data set. In particular, repeated calls to `add_data` are slow. Statistics::Descriptive::Discrete's `add_data` is optimized for speed. For a give number of data points, this module's run time will increase as the number of unique data values in the data set increases. For example, while this module runs about 10x the speed of Statistics::Descriptive::Full for an 8-bit data set, the run speed drops to about 3x for an equivalent sized 20-bit data set.

See sdd_prof.pl in the examples directory to play with profiling this module against Statistics::Descriptive::Full.

# METHODS

\$stat = Statistics::Descriptive::Discrete->new();

Create a new statistics object.

Adds data to the statistics object. Sets a flag so that the statistics will be recomputed the next time they're needed.

Adds data to the statistics object where every two elements are a value and a count (how many times did the value occur?) The above is equivalent to `\$stat->add_data(1,1,42,42,42);` Use this when your data is in a form isomorphic to (\$value, \$occurrence).

\$stat->max();

Returns the maximum value of the data set.

\$stat->min();

Returns the minimum value of the data set.

\$stat->mindex();

Returns the index of the minimum value of the data set. The index returned is the first occurence of the minimum value.

Note: the index is determined by the order data was added using add_data() or add_data_tuple(). It is meaningless in context of get_data() as get_data() does not return values in the same order in which they were added. This behavior is different than Statistics::Descriptive which does preserve order.

\$stat->maxdex();

Returns the index of the maximum value of the data set. The index returned is the first occurence of the maximum value.

Note: the index is determined by the order data was added using `add_data()` or `add_data_tuple()`. It is meaningless in context of `get_data()` as `get_data()` does not return values in the same order in which they were added. This behavior is different than Statistics::Descriptive which does preserve order.

\$stat->count();

Returns the total number of elements in the data set.

\$stat->uniq();

If called in scalar context, returns the total number of unique elements in the data set. For example, if your data set is (1,2,2,3,3,3), uniq will return 3.

If called in array context, returns an array of each data value in the data set in sorted order. In the above example, `@uniq = \$stats->uniq();` would return (1,2,3)

This function is specific to Statistics::Descriptive::Discrete and is not implemented in Statistics::Descriptive.

It is useful for getting a frequency distribution for each discrete value in the data the set:

``````   my \$stats = Statistics::Descriptive::Discrete->new();
my @bins = \$stats->uniq();
my \$f = \$stats->frequency_distribution_ref(\@bins);
for (sort {\$a <=> \$b} keys %\$f) {
print "value = \$_, count = \$f->{\$_}\n";
}``````
\$stat->sum();

Returns the sum of all the values in the data set.

\$stat->mean();

Returns the mean 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. Returns `undef` if any of the data are less than 0. Returns 0 if any of the data are 0.

\$stat->median();

Returns the median value of the data.

\$stat->mode();

Returns the mode of the data.

\$stat->variance();

Returns the variance of the data.

\$stat->standard_deviation();

Returns the standard_deviation of the data.

\$stat->sample_range();

Returns the sample range (max - min) of the data set.

\$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_ref(\@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::Discrete and using it is discouraged.

Note: in earlier versions of Statistics:Descriptive::Discrete, `frequency_distribution()` behaved differently than the Statistics::Descriptive implementation. Any code that uses this function should be carefully checked to ensure compatability with the current implementation.

\$stat->get_data();

Returns a copy of the data array. Note: This array could be very large and would thus defeat the purpose of using this module. Make sure you really need it before using get_data().

The returned array contains the values sorted by value. It does not preserve the order in which the values were added. Preserving order would defeat the purpose of this module which trades speed and memory usage over preserving order. If order is important, use Statistics::Descriptive.

\$stat->clear();

Clears all data and resets the instance as if it were newly created

Effectively the same as

``````  my \$class = ref(\$stat);
undef \$stat;
\$stat = new \$class;``````

# NOTE

The interface for this module strives to be identical to Statistics::Descriptive. Any differences are noted in the description for each method.

# BUGS

• Code for calculating mode is not as robust as it should be.

• Other bugs are lurking I'm sure.

# TODO

• Add rest of methods (at least ones that don't depend on original order of data) from Statistics::Descriptive

# AUTHOR

Rhet Turnbull, rturnbull+cpan@gmail.com

# CREDIT

Thanks to the following individuals for finding bugs, providing feedback, and submitting changes:

• Peter Dienes for finding and fixing a bug in the variance calculation.

• Bill Dueber for suggesting the add_data_tuple method.

``````  Copyright (c) 2002, 2019 Rhet Turnbull. All rights reserved.  This
program is free software; you can redistribute it and/or modify it
under the same terms as Perl itself.

Portions of this code is from Statistics::Descriptive which is under

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