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module analysis::statistics::Descriptive

rascal-0.40.16

Descriptive Statistics.

Usage​

import analysis::statistics::Descriptive;

Dependencies​

import Exception;
import util::Math;
import List;

Description​

Provides the following univariate (single variable) statistics functions:

Examples​

rascal>import analysis::statistics::Descriptive;
ok
rascal>D = [67, 88, 55, 92.5, 102, 51];
list[num]: [67,88,55,92.5,102,51]
rascal>mn = min(D);
num: 51
rascal>mx = max(D);
num: 102
rascal>range = mx - mn;
num: 51
rascal>midrange =  mn + range/2;
num: 76.5
rascal>sum(D);
num: 455.5
rascal>mean(D);
real: 75.91666667
rascal>geometricMean(D);
real: 73.3734107237
rascal>standardDeviation(D);
real: 21.1622698845
rascal>variance(D);
num: 447.841666666666666666666666666
rascal>percentile(D,25);
num: 55
rascal>percentile(D,50);
num: 67
rascal>percentile(D,75);
num: 92.5

function geometricMean​

Geometric mean of data values.

real geometricMean([num hd, *num tl])

Computes the geometric mean of the given data values.

function kurtosis​

Kurtosis of data values.

real kurtosis(list[num] values:[_, *_])

Computes the kurtosis of the given data values. Kurtosis is a measure of the "peakedness" of a distribution.

function kurtosisExcess​

Kurtosis excess of data values.

real kurtosisExcess(list[num] values)

Computes the kurtosis excess of the given data values. Kurtosis excess is a measure of the "peakedness" of a distribution corrected such that a normal distribution will be 0.

function max​

Largest data value.

(&T <: num) max([(&T <: num) h, *(&T <: num) t])

function mean​

Arithmetic mean of data values.

real mean(list[num] nums:[_, *_])

Computes the arithmetic mean of the data values.

function median​

Median of data values.

default real median(list[num] nums:[_, *_])

Returns the median of the available values. This is the same as the 50th Percentile.

Examples​

rascal>import analysis::statistics::Descriptive;
ok
rascal>median([1,2,5,7,8]);
real: 5.
rascal>median([1,2,2,6,7,8]);
real: 4.

function middle​

list[&T] middle(list[&T] nums)

function min​

Smallest data value.

(&T <: num) min([(&T <: num) h, *(&T <: num) t])

function percentile​

Percentile of data values.

&T <: num percentile(list[&T <: num] nums, num p)

Returns the pth percentile of the data values. 0 < p <= 100 should hold.

function variance​

Variance of data values.

num variance([num hd, *num tl])

Computes the variance of the data values. It measures how far a set of numbers is spread out.

function skewness​

Skewness of data values.

real skewness(list[num] values:[_, *_])

Returns the skewness of the available values. Skewness is a measure of the asymmetry of a given distribution.

function standardDeviation​

Standard deviation of data values.

real standardDeviation(list[num] values)

Computes the standard deviation of the data values. It shows how much variation exists from the average (mean, or expected value).

function sum​

Sum of data values.

(&T <:num) sum([(&T <: num) hd, *(&T <: num) tl])

function sumsq​

Sum of the squares of data values.

(&T <:num) sumsq(list[&T <:num] values)

function centralMoment​

Calculate the k-th central moment.

real centralMoment(list[num] nums:[_, *_], int order = 1)

function moment​

Calculate the k-th moment.

real moment(list[num] nums:[_, *_], int order = 1)