.. _library_statistics:

statistics

The entities in this library define some useful predicates for descriptive statistics. Data is represented as a list of numbers (integers or floats). Use the object sample if your data represents a sample. Use the object population if your data represents a population.

The variance/2, standard_deviation/2, skewness/2, kurtosis/2, covariance/3, standard_error/2, correlation/3, and rank_correlation/3 predicates use different formulas depending on whether the data represents a sample (dividing by N-1) or a population (dividing by N). All other predicates share the same implementation.

API documentation

Open the `../../apis/library_index.html#statistics <../../apis/library_index.html#statistics>`__ link in a web browser.

Loading

To load all entities in this library, load the loader.lgt file:

::

| ?- logtalk_load(statistics(loader)).

Testing

To test this library predicates, load the tester.lgt file:

::

| ?- logtalk_load(statistics(tester)).

API overview

Aggregation ~~~~~~~~~~~

============= =========================== Predicate Description ============= =========================== product/2 Product of all list numbers sum/2 Sum of all list numbers ============= ===========================

Extremes and Range ~~~~~~~~~~~~~~~~~~

============= ========================== Predicate Description ============= ========================== min/2 Minimum value max/2 Maximum value min_max/3 Minimum and maximum values range/2 Range (max - min) ============= ==========================

Central Tendency ~~~~~~~~~~~~~~~~

+-----------------------+----------------------------------------------+ | Predicate | Description | +=======================+==============================================+ | arithmetic_mean/2 | Arithmetic mean | +-----------------------+----------------------------------------------+ | geometric_mean/2 | Geometric mean | +-----------------------+----------------------------------------------+ | harmonic_mean/2 | Harmonic mean | +-----------------------+----------------------------------------------+ | weighted_mean/3 | Weighted mean | +-----------------------+----------------------------------------------+ | trimmed_mean/3 | Trimmed mean (removing a fraction of extreme | | | values) | +-----------------------+----------------------------------------------+ | median/2 | Median | +-----------------------+----------------------------------------------+ | modes/2 | Modes (in ascending order) | +-----------------------+----------------------------------------------+

.. _measures-of-position--quantiles:

Measures of Position / Quantiles ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

+---------------------------+------------------------------------------+ | Predicate | Description | +===========================+==========================================+ | fractile/3 | Fractile (quantile given a fraction in | | | (0.0, 1.0)) | +---------------------------+------------------------------------------+ | percentile/3 | Percentile (quantile given a value in | | | (0, 100)) | +---------------------------+------------------------------------------+ | quartiles/4 | Quartiles (Q1, Q2, Q3) | +---------------------------+------------------------------------------+ | interquartile_range/2 | Interquartile range (Q3 - Q1) | +---------------------------+------------------------------------------+

Measures of Dispersion ~~~~~~~~~~~~~~~~~~~~~~

+-----------------------------------+----------------------------------+ | Predicate | Description | +===================================+==================================+ | variance/2 | Variance (sample or population) | +-----------------------------------+----------------------------------+ | standard_deviation/2 | Standard deviation (sample or | | | population) | +-----------------------------------+----------------------------------+ | mean_deviation/2 | Mean absolute deviation | +-----------------------------------+----------------------------------+ | median_deviation/2 | Median absolute deviation | +-----------------------------------+----------------------------------+ | average_deviation/3 | Average absolute deviation from | | | a given central tendency | +-----------------------------------+----------------------------------+ | coefficient_of_variation/2 | Coefficient of variation | +-----------------------------------+----------------------------------+ | relative_standard_deviation/2 | Relative standard deviation | | | (percentage) | +-----------------------------------+----------------------------------+ | sum_of_squares/2 | Sum of squared deviations from | | | the mean | +-----------------------------------+----------------------------------+ | standard_error/2 | Standard error of the mean | +-----------------------------------+----------------------------------+

Measures of Shape ~~~~~~~~~~~~~~~~~

==================== ====================================== Predicate Description ==================== ====================================== skewness/2 Moment skewness (sample or population) kurtosis/2 Excess kurtosis (sample or population) central_moment/3 K-th central moment ==================== ======================================

Measures of Association ~~~~~~~~~~~~~~~~~~~~~~~

====================== ===================================== Predicate Description ====================== ===================================== covariance/3 Covariance (sample or population) correlation/3 Pearson correlation coefficient rank_correlation/3 Spearman rank correlation coefficient ====================== =====================================

Error Metrics

============================= =========================================
Predicate                     Description
============================= =========================================
``mean_squared_error/3``      Mean squared error between two lists
``root_mean_squared_error/3`` Root mean squared error between two lists
============================= =========================================

Normalization

=========================== =========================================== Predicate Description =========================== =========================================== z_normalization/2 Z-score normalization (mean ~= 0, std ~= 1) min_max_normalization/2 Min-max normalization (rescale to [0, 1]) =========================== ===========================================

.. _frequency--counting:

Frequency / Counting ~~~~~~~~~~~~~~~~~~~~

============================ ========================================== Predicate Description ============================ ========================================== frequency_distribution/2 Frequency distribution (Value-Count pairs) ============================ ==========================================

Validation ~~~~~~~~~~

=========== ================================ Predicate Description =========== ================================ valid/1 Term is a closed list of numbers =========== ================================