.. index:: statisticsp
.. _statisticsp/0:

**protocol**

``statisticsp``
===============

Statistical calculations over a list of numbers protocol.

| **Author:** Paulo Moura
| **Version:** 1.1
| **Date:** 2017/10/3

| **Compilation flags:**
|    ``static``


(no dependencies on other entities)


Public interface
----------------

.. raw:: html

   <div id="product/2"> </div>

.. index:: product/2
.. _statisticsp/0::product/2:

``product/2``
^^^^^^^^^^^^^

Calculates the product of all list numbers. Fails if the list is empty.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``product(List,Product)``
| **Mode and number of proofs:**
|    ``product(+list(number),-number)`` - ``zero_or_one``


.. raw:: html

   <div id="sum/2"> </div>

.. index:: sum/2
.. _statisticsp/0::sum/2:

``sum/2``
^^^^^^^^^

Calculates the sum of all list numbers. Fails if the list is empty.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``sum(List,Sum)``
| **Mode and number of proofs:**
|    ``sum(+list(number),-number)`` - ``zero_or_one``


.. raw:: html

   <div id="max/2"> </div>

.. index:: max/2
.. _statisticsp/0::max/2:

``max/2``
^^^^^^^^^

Determines the list maximum value in a list of numbers. Fails if the list is empty.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``max(List,Maximum)``
| **Mode and number of proofs:**
|    ``max(+list,-number)`` - ``zero_or_one``


.. raw:: html

   <div id="min/2"> </div>

.. index:: min/2
.. _statisticsp/0::min/2:

``min/2``
^^^^^^^^^

Determines the minimum value in a list of numbers. Fails if the list is empty.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``min(List,Minimum)``
| **Mode and number of proofs:**
|    ``min(+list,-number)`` - ``zero_or_one``


.. raw:: html

   <div id="range/2"> </div>

.. index:: range/2
.. _statisticsp/0::range/2:

``range/2``
^^^^^^^^^^^

Range is the length of the smallest interval which contains all the numbers in List. Fails if the list is empty.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``range(List,Range)``
| **Mode and number of proofs:**
|    ``range(+list,-number)`` - ``zero_or_one``


.. raw:: html

   <div id="arithmetic_mean/2"> </div>

.. index:: arithmetic_mean/2
.. _statisticsp/0::arithmetic_mean/2:

``arithmetic_mean/2``
^^^^^^^^^^^^^^^^^^^^^

Calculates the arithmetic mean of a list of numbers. Fails if the list is empty.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``arithmetic_mean(List,Mean)``
| **Mode and number of proofs:**
|    ``arithmetic_mean(+list(number),-float)`` - ``zero_or_one``


.. raw:: html

   <div id="geometric_mean/2"> </div>

.. index:: geometric_mean/2
.. _statisticsp/0::geometric_mean/2:

``geometric_mean/2``
^^^^^^^^^^^^^^^^^^^^

Calculates the geometric mean of a list of numbers. Fails if the list is empty.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``geometric_mean(List,Mean)``
| **Mode and number of proofs:**
|    ``geometric_mean(+list(number),-float)`` - ``zero_or_one``


.. raw:: html

   <div id="harmonic_mean/2"> </div>

.. index:: harmonic_mean/2
.. _statisticsp/0::harmonic_mean/2:

``harmonic_mean/2``
^^^^^^^^^^^^^^^^^^^

Calculates the harmonic mean of a list of numbers. Fails if the list is empty.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``harmonic_mean(List,Mean)``
| **Mode and number of proofs:**
|    ``harmonic_mean(+list(number),-float)`` - ``zero_or_one``


.. raw:: html

   <div id="median/2"> </div>

.. index:: median/2
.. _statisticsp/0::median/2:

``median/2``
^^^^^^^^^^^^

Calculates the median of a list of numbers. Fails if the list is empty.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``median(List,Median)``
| **Mode and number of proofs:**
|    ``median(+list(number),-float)`` - ``zero_or_one``


.. raw:: html

   <div id="average_deviation/3"> </div>

.. index:: average_deviation/3
.. _statisticsp/0::average_deviation/3:

``average_deviation/3``
^^^^^^^^^^^^^^^^^^^^^^^

Calculates the average absolute deviation of a list of numbers given a central tendency (e.g. mean, median, or mode). Fails if the list is empty.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``average_deviation(List,CentralTendency,Deviation)``
| **Mode and number of proofs:**
|    ``average_deviation(+list(number),+float,-float)`` - ``zero_or_one``


.. raw:: html

   <div id="mean_deviation/2"> </div>

.. index:: mean_deviation/2
.. _statisticsp/0::mean_deviation/2:

``mean_deviation/2``
^^^^^^^^^^^^^^^^^^^^

Calculates the mean absolute deviation of a list of numbers. Fails if the list is empty.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``mean_deviation(List,Deviation)``
| **Mode and number of proofs:**
|    ``mean_deviation(+list(number),-float)`` - ``zero_or_one``


.. raw:: html

   <div id="median_deviation/2"> </div>

.. index:: median_deviation/2
.. _statisticsp/0::median_deviation/2:

``median_deviation/2``
^^^^^^^^^^^^^^^^^^^^^^

Calculates the median absolute deviation of a list of numbers. Fails if the list is empty.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``median_deviation(List,Deviation)``
| **Mode and number of proofs:**
|    ``median_deviation(+list(number),-float)`` - ``zero_or_one``


.. raw:: html

   <div id="standard_deviation/2"> </div>

.. index:: standard_deviation/2
.. _statisticsp/0::standard_deviation/2:

``standard_deviation/2``
^^^^^^^^^^^^^^^^^^^^^^^^

Calculates the standard deviation of a list of numbers. Fails if the list is empty.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``standard_deviation(List,Deviation)``
| **Mode and number of proofs:**
|    ``standard_deviation(+list(number),-float)`` - ``zero_or_one``


.. raw:: html

   <div id="coefficient_of_variation/2"> </div>

.. index:: coefficient_of_variation/2
.. _statisticsp/0::coefficient_of_variation/2:

``coefficient_of_variation/2``
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Calculates the coefficient of variation of a list of numbers. Fails if the list is empty.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``coefficient_of_variation(List,Coefficient)``
| **Mode and number of proofs:**
|    ``coefficient_of_variation(+list(number),-float)`` - ``zero_or_one``


.. raw:: html

   <div id="relative_standard_deviation/2"> </div>

.. index:: relative_standard_deviation/2
.. _statisticsp/0::relative_standard_deviation/2:

``relative_standard_deviation/2``
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Calculates the relative standard deviation of a list of numbers. Fails if the list is empty.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``relative_standard_deviation(List,Percentage)``
| **Mode and number of proofs:**
|    ``relative_standard_deviation(+list(number),-float)`` - ``zero_or_one``


.. raw:: html

   <div id="skewness/2"> </div>

.. index:: skewness/2
.. _statisticsp/0::skewness/2:

``skewness/2``
^^^^^^^^^^^^^^

Calculates the (moment) skewness of a list of numbers. Fails if the list is empty.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``skewness(List,Skewness)``
| **Mode and number of proofs:**
|    ``skewness(+list(number),-float)`` - ``zero_or_one``


.. raw:: html

   <div id="kurtosis/2"> </div>

.. index:: kurtosis/2
.. _statisticsp/0::kurtosis/2:

``kurtosis/2``
^^^^^^^^^^^^^^

Calculates the (excess) kurtosis of a list of numbers. Fails if the list is empty.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``kurtosis(List,Kurtosis)``
| **Mode and number of proofs:**
|    ``kurtosis(+list(number),-float)`` - ``zero_or_one``


.. raw:: html

   <div id="variance/2"> </div>

.. index:: variance/2
.. _statisticsp/0::variance/2:

``variance/2``
^^^^^^^^^^^^^^

Calculates the unbiased variance of a list of numbers. Fails if the list is empty.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``variance(List,Variance)``
| **Mode and number of proofs:**
|    ``variance(+list(number),-float)`` - ``zero_or_one``


.. raw:: html

   <div id="z_normalization/2"> </div>

.. index:: z_normalization/2
.. _statisticsp/0::z_normalization/2:

``z_normalization/2``
^^^^^^^^^^^^^^^^^^^^^

Normalizes a list of number such that for the resulting list the mean of is close to zero and the standard deviation is close to 1. Fails if the list is empty.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``z_normalization(List,NormalizedList)``
| **Mode and number of proofs:**
|    ``z_normalization(+list(number),-list(float))`` - ``zero_or_one``


.. raw:: html

   <div id="valid/1"> </div>

.. index:: valid/1
.. _statisticsp/0::valid/1:

``valid/1``
^^^^^^^^^^^

Term is a closed list of numbers.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``valid(Term)``
| **Mode and number of proofs:**
|    ``valid(@nonvar)`` - ``zero_or_one``


Protected interface
-------------------

(none)

Private predicates
------------------

.. raw:: html

   <div id="arithmetic_mean/5"> </div>

.. index:: arithmetic_mean/5
.. _statisticsp/0::arithmetic_mean/5:

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

| **Compilation flags:**
|    ``static``


.. raw:: html

   <div id="squares_and_cubes/6"> </div>

.. index:: squares_and_cubes/6
.. _statisticsp/0::squares_and_cubes/6:

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

| **Compilation flags:**
|    ``static``


.. raw:: html

   <div id="squares_and_hypers/6"> </div>

.. index:: squares_and_hypers/6
.. _statisticsp/0::squares_and_hypers/6:

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

| **Compilation flags:**
|    ``static``


.. raw:: html

   <div id="variance/6"> </div>

.. index:: variance/6
.. _statisticsp/0::variance/6:

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

| **Compilation flags:**
|    ``static``


Operators
---------

(none)

Remarks
-------

(none)

.. seealso::

   :ref:`statistics <statistics/0>`, :ref:`sample <sample/0>`, :ref:`population <population/0>`

