.. index:: single: statistics .. _statistics/0:

.. rst-class:: right

category

statistics

Statistical calculations over a list of numbers.

| Availability: | logtalk_load(statistics(loader))

| Author: Paulo Moura | Version: 1:8:0 | Date: 2026-02-20

| Compilation flags: | static

| Implements: | public :ref:`statisticsp <statisticsp/0>` | Uses: | :ref:`list <list/0>` | :ref:`numberlist <numberlist/0>`

| Remarks: | (none)

| Inherited public predicates: |  :ref:`statisticsp/0::arithmetic_mean/2`  :ref:`statisticsp/0::average_deviation/3`  :ref:`statisticsp/0::central_moment/3`  :ref:`statisticsp/0::coefficient_of_variation/2`  :ref:`statisticsp/0::correlation/3`  :ref:`statisticsp/0::covariance/3`  :ref:`statisticsp/0::fractile/3`  :ref:`statisticsp/0::frequency_distribution/2`  :ref:`statisticsp/0::geometric_mean/2`  :ref:`statisticsp/0::harmonic_mean/2`  :ref:`statisticsp/0::interquartile_range/2`  :ref:`statisticsp/0::kurtosis/2`  :ref:`statisticsp/0::max/2`  :ref:`statisticsp/0::mean_deviation/2`  :ref:`statisticsp/0::mean_squared_error/3`  :ref:`statisticsp/0::median/2`  :ref:`statisticsp/0::median_deviation/2`  :ref:`statisticsp/0::min/2`  :ref:`statisticsp/0::min_max/3`  :ref:`statisticsp/0::min_max_normalization/2`  :ref:`statisticsp/0::modes/2`  :ref:`statisticsp/0::percentile/3`  :ref:`statisticsp/0::product/2`  :ref:`statisticsp/0::quartiles/4`  :ref:`statisticsp/0::range/2`  :ref:`statisticsp/0::rank_correlation/3`  :ref:`statisticsp/0::relative_standard_deviation/2`  :ref:`statisticsp/0::root_mean_squared_error/3`  :ref:`statisticsp/0::skewness/2`  :ref:`statisticsp/0::standard_deviation/2`  :ref:`statisticsp/0::standard_error/2`  :ref:`statisticsp/0::sum/2`  :ref:`statisticsp/0::sum_of_squares/2`  :ref:`statisticsp/0::trimmed_mean/3`  :ref:`statisticsp/0::valid/1`  :ref:`statisticsp/0::variance/2`  :ref:`statisticsp/0::weighted_mean/3`  :ref:`statisticsp/0::z_normalization/2`  

.. contents:: :local: :backlinks: top

Public predicates

(no local declarations; see entity ancestors if any)

Protected predicates

(no local declarations; see entity ancestors if any)

Private predicates

.. index:: arithmetic_mean/5 .. _statistics/0::arithmetic_mean/5:

arithmetic_mean/5 ^^^^^^^^^^^^^^^^^^^^^

Auxiliary predicate for computing the arithmetic mean.

| Compilation flags: | static

| Template: | arithmetic_mean(List,Length0,Length,Sum,Mean) | Mode and number of proofs: | arithmetic_mean(+list(number),+integer,-integer,+number,-float) - one

---

.. index:: squares_and_cubes/6 .. _statistics/0::squares_and_cubes/6:

squares_and_cubes/6 ^^^^^^^^^^^^^^^^^^^^^^^

Auxiliary predicate for computing the skewness.

| Compilation flags: | static

| Template: | squares_and_cubes(List,Mean,Squares0,Squares,Cubes0,Cubes) | Mode and number of proofs: | squares_and_cubes(+list(number),+float,+float,-float,+float,-float) - one

---

.. index:: squares_and_hypers/6 .. _statistics/0::squares_and_hypers/6:

squares_and_hypers/6 ^^^^^^^^^^^^^^^^^^^^^^^^

Auxiliary predicate for computing the kurtosis.

| Compilation flags: | static

| Template: | squares_and_hypers(List,Mean,Squares0,Squares,Hypers0,Hypers) | Mode and number of proofs: | squares_and_hypers(+list(number),+float,+float,-float,+float,-float) - one

---

.. index:: variance/6 .. _statistics/0::variance/6:

variance/6 ^^^^^^^^^^^^^^

Auxiliary predicate for computing the variance.

| Compilation flags: | static

| Template: | variance(List,Length0,Length,Mean,M20,M2) | Mode and number of proofs: | variance(+list(number),+integer,-integer,+float,+float,-float) - one

---

.. index:: cross_deviation_sum/6 .. _statistics/0::cross_deviation_sum/6:

cross_deviation_sum/6 ^^^^^^^^^^^^^^^^^^^^^^^^^

Auxiliary predicate for computing the cross-deviation sum for covariance.

| Compilation flags: | static

| Template: | cross_deviation_sum(List1,List2,Mean1,Mean2,Sum0,Sum) | Mode and number of proofs: | cross_deviation_sum(+list(number),+list(number),+float,+float,+float,-float) - one

---

.. index:: sorted_median/3 .. _statistics/0::sorted_median/3:

sorted_median/3 ^^^^^^^^^^^^^^^^^^^

Auxiliary predicate for computing the median of an already sorted list with known length.

| Compilation flags: | static

| Template: | sorted_median(Sorted,Length,Median) | Mode and number of proofs: | sorted_median(+list(number),+integer,-number) - one

---

.. index:: sum_of_squares/4 .. _statistics/0::sum_of_squares/4:

sum_of_squares/4 ^^^^^^^^^^^^^^^^^^^^

Auxiliary predicate for computing the sum of squared deviations.

| Compilation flags: | static

| Template: | sum_of_squares(List,Mean,Sum0,Sum) | Mode and number of proofs: | sum_of_squares(+list(number),+float,+float,-float) - one

---

.. index:: central_moment_sum/7 .. _statistics/0::central_moment_sum/7:

central_moment_sum/7 ^^^^^^^^^^^^^^^^^^^^^^^^

Auxiliary predicate for computing central moments.

| Compilation flags: | static

| Template: | central_moment_sum(List,K,Mean,N0,Sum0,N,Sum) | Mode and number of proofs: | central_moment_sum(+list(number),+positive_integer,+float,+integer,+float,-integer,-float) - one

---

.. index:: min_max_normalize/4 .. _statistics/0::min_max_normalize/4:

min_max_normalize/4 ^^^^^^^^^^^^^^^^^^^^^^^

Auxiliary predicate for min-max normalization.

| Compilation flags: | static

| Template: | min_max_normalize(List,Min,Range,NormalizedList) | Mode and number of proofs: | min_max_normalize(+list(number),+number,+number,-list(float)) - one

---

.. index:: count_frequencies/4 .. _statistics/0::count_frequencies/4:

count_frequencies/4 ^^^^^^^^^^^^^^^^^^^^^^^

Auxiliary predicate for computing frequency distribution.

| Compilation flags: | static

| Template: | count_frequencies(List,CurrentValue,CurrentCount,Distribution) | Mode and number of proofs: | count_frequencies(+list(number),+number,+integer,-list(pair(number,integer))) - one

---

.. index:: squared_error_sum/6 .. _statistics/0::squared_error_sum/6:

squared_error_sum/6 ^^^^^^^^^^^^^^^^^^^^^^^

Auxiliary predicate for computing mean squared error.

| Compilation flags: | static

| Template: | squared_error_sum(List1,List2,N0,Sum0,N,Sum) | Mode and number of proofs: | squared_error_sum(+list(number),+list(number),+integer,+float,-integer,-float) - one

---

.. index:: compute_ranks/3 .. _statistics/0::compute_ranks/3:

compute_ranks/3 ^^^^^^^^^^^^^^^^^^^

Auxiliary predicate for computing ranks of elements in a list.

| Compilation flags: | static

| Template: | compute_ranks(List,All,Ranks) | Mode and number of proofs: | compute_ranks(+list(number),+list(number),-list(float)) - one

---

.. index:: count_less_equal/6 .. _statistics/0::count_less_equal/6:

count_less_equal/6 ^^^^^^^^^^^^^^^^^^^^^^

Auxiliary predicate for counting elements less than and equal to a value.

| Compilation flags: | static

| Template: | count_less_equal(List,Value,Less0,Less,Equal0,Equal) | Mode and number of proofs: | count_less_equal(+list(number),+number,+integer,-integer,+integer,-integer) - one

---

Operators

(none)