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`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

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

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

Validation

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