protocol

# `statisticsp`

Statistical calculations over a list of numbers protocol.

Author: Paulo Moura
Version: 1:3:0
Date: 2022-06-20
Compilation flags:
`static`
Dependencies:
(none)
Remarks:
(none)
Inherited public predicates:
(none)

## Public predicates

### `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`

### `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`

### `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`

### `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`

### `min_max/3`

Determines the minimum and maxium values in a list of numbers. Fails if the list is empty.

Compilation flags:
`static`
Template:
`min_max(List,Minimum,Maximum)`
Mode and number of proofs:
`min_max(+list(number),-number,-number)` - `zero_or_one`

### `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`

### `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`

### `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`

### `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`

### `weighted_mean/3`

Calculates the weighted mean of a list of numbers. Fails if the list is empty or if the two lists have different lengths. Wights are assume to be non-negative.

Compilation flags:
`static`
Template:
`weighted_mean(Weights,List,Mean)`
Mode and number of proofs:
`weighted_mean(+list(number),+list(number),-float)` - `zero_or_one`

### `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`

### `modes/2`

Returns the list of modes of a list of numbers in ascending order. Fails if the list is empty.

Compilation flags:
`static`
Template:
`modes(List,Modes)`
Mode and number of proofs:
`modes(+list(number),-list(number))` - `zero_or_one`

### `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`

### `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`

### `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`

### `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`

### `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`

### `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`

### `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`

### `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`

### `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`

### `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`

### `fractile/3`

Calculates the smalest value in a list of numbers such that the list elements in its fraction `P` are less or equal to that value (with `P` in the open interval `(0.0, 1.0)`). Fails if the list is empty.

Compilation flags:
`static`
Template:
`fractile(P,List,Fractile)`
Mode and number of proofs:
`fractile(+float,+list(integer),-integer)` - `zero_or_one`
`fractile(+float,+list(float),-float)` - `zero_or_one`

### `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`

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