Statistics::Distributions

Raku package for statistical distributions and related random variates generations.

The distributions and random variate functions of the generations of "Statistics::Distributions" are automatically exported when "Data::Generators", [AAp1] is loaded.

Installation

From Zef ecosystem:

zef install Statistics::Distributions

From GitHub:

zef install https://github.com/antononcube/Raku-Statistics-Distributions.git

Random reals

This module provides the function random-real that can be used to generate lists of real numbers using the uniform distribution.

Here is a random real:

use Statistics::Distributions;
say random-real(); 

# 0.7566029477029932

Here is a random real between 0 and 20:

say random-real(20); 

# 7.782185548019564

Here are six random reals between -2 and 12:

say random-real([-2,12], 6);

# (5.984218977817309 -0.7470893085067976 0.9036675312487041 2.5560218342093943 -1.910581002606549 7.685430947831199)

Here is a 4-by-3 array of random reals between -3 and 3:

say random-real([-3,3], [4,3]);

# [[-2.7840704028823544 0.8287109105292263 2.558504357563728]
#  [-1.0941755936293156 0.8651999088838096 -0.9438774646497903]
#  [1.1212043168666623 2.752612228122736 2.482152045517397]
#  [2.80676721650401 -2.970465529169304 -2.4619764627222165]]

Remark: The signature design follows Mathematica's function RandomReal.

Random variates

This module provides the function random-variate that can be used to generate lists of real numbers using distribution specifications.

Here are examples:

say random-variate(BernoulliDistribution.new(:p(0.3)), 1000).BagHash.Hash; 

# {0 => 680, 1 => 320}

say random-variate(BinomialDistribution.new(:n(10), :p(0.2)), 10); 

# (1 5 3 2 2 2 8 1 1 1)

say random-variate(NormalDistribution.new( µ => 10, σ => 20), 5); 

# (-40.1003663069411 -21.037958898210185 11.71662526417637 -15.783821746585186 14.583792668629403)

say random-variate(UniformDistribution.new(:min(2), :max(60)), 5);

# (24.16922574013087 18.852280485082424 16.837079621903225 45.84863399963783 14.405878874364358)

Remark: Only Normal distribution and Uniform distribution are implemented at this point.

Remark: The signature design follows Mathematica's function RandomVariate.

Here is an example of 2D array generation:

say random-variate(NormalDistribution.new, [3,4]);

# [[0.01191681514433013 -1.0665450738906437 0.5102179377029749 -2.2758079566657665]
#  [-1.226596770652097 -0.7170922416291008 -1.6924928241645187 -0.3585903281924563]
#  [-0.3979421974219298 -0.8014262498733147 0.21027706617767977 0.19396187939866336]]

Remark: The Markdown document "Random-variate-generation-examples.md", is a guide to generating random variates with the distributions of this package.

Quantile calculations with different methods

The sub quantile provided by the package can take parameters that cover 10 different methods commonly used in statistics. (That is similar to Quantile, [WRI1], of Wolfram Language.)

For example:

my @values = 3.2, 1.5, 7.8, 4.1, 9.9, 2.3, 6.5, 0.8, 5.5, 8.7;
quantile(@values, probs => (0.2, 0.4 ... 0.8), params => [[0,1],[0,1]])

# [1.66 3.56 6.1 8.52]

References

[AAp1] Anton Antonov Data::Generators Raku package, (2021-2024), GitHub/antononcube.

[WRI1] Wolfram Research, Quantile, Wolfram Language function, (2003), (updated 2024).