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NAME
====
Math::Libgsl::Statistics - An interface to libgsl, the Gnu Scientific Library - Statistics
SYNOPSIS
========
```raku
use Math::Libgsl::Statistics;
my @data = ^10;
say "mean = { mean(@data) }, variance = { variance(@data) }";
```
DESCRIPTION
===========
Math::Libgsl::Statistics is an interface to the Statistics functions of libgsl, the Gnu Scientific Library.
The functions in this module come in 10 data types:
* Math::Libgsl::Statistics (default: num64)
* Math::Libgsl::Statistics::Num32
* Math::Libgsl::Statistics::Int8
* Math::Libgsl::Statistics::Int16
* Math::Libgsl::Statistics::Int32
* Math::Libgsl::Statistics::Int64
* Math::Libgsl::Statistics::UInt8
* Math::Libgsl::Statistics::UInt16
* Math::Libgsl::Statistics::UInt32
* Math::Libgsl::Statistics::UInt64
All the following functions are available in the modules correspondiing to each datatype, except where noted.
### mean(@data!, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Num)
This function returns the arithmetic mean of @data.
### variance(@data!, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Num)
This function returns the estimated variance of @data. This function computes the mean, if you already computed the mean, use the next function.
### variance-m(@data!, Num() $mean!, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride)
This function returns the sample variance of @data relative to the given value of $mean.
### sd(@data!, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Num)
This function returns the estimated standard deviation of @data.
### sd-m(@data!, Num() $mean!, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Num)
This function returns the sample standard deviation of @data relative to the given value of $mean.
### tss(@data!, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Num)
These functions return the total sum of squares (TSS) of @data.
### tss-m(@data!, Num() $mean!, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Num)
These functions return the total sum of squares (TSS) of @data relative to the given value of $mean.
### variance-with-fixed-mean(@data!, Num() $mean!, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Num)
This function computes an unbiased estimate of the variance of @data when the population mean $mean of the underlying distribution is known a priori.
### sd-with-fixed-mean(@data!, Num() $mean!, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Num)
This function calculates the standard deviation of @data for a fixed population mean $mean.
### absdev(@data!, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Num)
This function computes the absolute deviation from the mean of @data.
### absdev-m(@data!, Num() $mean!, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Num)
This function computes the absolute deviation of the dataset @data relative to the given value of $mean.
### skew(@data!, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Num)
This function computes the skewness of @data.
### skew-m-sd(@data!, Num() $mean!, Num() $sd!, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Num)
This function computes the skewness of the dataset @data using the given values of the mean $mean and standard deviation $sd,
### kurtosis(@data!, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Num)
This function computes the kurtosis of @data.
### kurtosis-m-sd(@data!, Num() $mean!, Num() $sd!, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Num)
This function computes the kurtosis of the dataset @data using the given values of the mean $mean and standard deviation $sd,
### autocorrelation(@data!, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Num)
This function computes the lag-1 autocorrelation of the dataset @data.
### autocorrelation-m(@data!, Num() $mean!, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Num)
This function computes the lag-1 autocorrelation of the dataset @data using the given value of the mean $mean.
### covariance(@data1!, @data2! where *.elems == @data1.elems, Int() :$stride1? = 1, Int() :$stride2? = 1, Int() :$n? = (@data1.elems / $stride1).Int --> Num)
This function computes the covariance of the datasets @data1 and @data2.
### covariance-m(@data1!, @data2! where *.elems == @data1.elems, Num() $mean1!, Num() $mean2!, Int() :$stride1? = 1, Int() :$stride2? = 1, Int() :$n? = (@data1.elems / $stride1).Int --> Num)
This function computes the covariance of the datasets @data1 and @data2 using the given values of the means, $mean1 and $mean2.
### correlation(@data1!, @data2! where *.elems == @data1.elems, Int() :$stride1? = 1, Int() :$stride2? = 1, Int() :$n? = (@data1.elems / $stride1).Int --> Num)
This function efficiently computes the Pearson correlation coefficient between the datasets @data1 and @data2.
### spearman(@data1!, @data2! where *.elems == @data1.elems, Int() :$stride1? = 1, Int() :$stride2? = 1, Int() :$n? = (@data1.elems / $stride1).Int --> Num)
This function computes the Spearman rank correlation coefficient between the datasets @data1 and @data2.
### wmean(@w!, @data!, Int() :$wstride? = 1, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Num)
This function returns the weighted mean of the dataset @data using the set of weights @w. This function is available only for Numeric types, so only when using Math::Libgsl::Statistics or Math::Libgsl::Statistics::Num32.
### wvariance(@w!, @data!, Int() :$wstride? = 1, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Num)
This function returns the estimated variance of the dataset @data using the set of weights @w. This function is available only for Numeric types, so only when using Math::Libgsl::Statistics or Math::Libgsl::Statistics::Num32.
### wvariance-m(@w!, @data!, Num() $wmean!, Int() :$wstride? = 1, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Num)
This function returns the estimated variance of the weighted dataset @data using the given weighted mean $wmean. This function is available only for Numeric types, so only when using Math::Libgsl::Statistics or Math::Libgsl::Statistics::Num32.
### wsd(@w!, @data!, Int() :$wstride? = 1, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Num)
This function returns the standard deviation of the weighted dataset @data. This function is available only for Numeric types, so only when using Math::Libgsl::Statistics or Math::Libgsl::Statistics::Num32.
### wsd-m(@w!, @data!, Num() $wmean!, Int() :$wstride? = 1, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Num)
This function returns the standard deviation of the weighted dataset @data using the given weighted mean $wmean. This function is available only for Numeric types, so only when using Math::Libgsl::Statistics or Math::Libgsl::Statistics::Num32.
### wvariance-with-fixed-mean(@w!, @data!, Num() $mean!, Int() :$wstride? = 1, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Num)
This function computes an unbiased estimate of the variance of the weighted dataset @data when the population mean $mean of the underlying distribution is known a priori. This function is available only for Numeric types, so only when using Math::Libgsl::Statistics or Math::Libgsl::Statistics::Num32.
### wsd-with-fixed-mean(@w!, @data!, Num() $mean!, Int() :$wstride? = 1, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Num)
This function computes an unbiased estimate of the standard deviation of the weighted dataset @data when the population mean $mean of the underlying distribution is known a priori. This function is available only for Numeric types, so only when using Math::Libgsl::Statistics or Math::Libgsl::Statistics::Num32.
### wtss(@w!, @data!, Int() :$wstride? = 1, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Num)
These functions return the weighted total sum of squares (TSS) of @data. This function is available only for Numeric types, so only when using Math::Libgsl::Statistics or Math::Libgsl::Statistics::Num32.
### wtss-m(@w!, @data!, Num() $wmean!, Int() :$wstride? = 1, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Num)
These functions return the weighted total sum of squares (TSS) of @data when the population mean $mean of the underlying distribution is known a priori. This function is available only for Numeric types, so only when using Math::Libgsl::Statistics or Math::Libgsl::Statistics::Num32.
### wabsdev(@w!, @data!, Int() :$wstride? = 1, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Num)
This function computes the weighted absolute deviation from the weighted mean of @data. This function is available only for Numeric types, so only when using Math::Libgsl::Statistics or Math::Libgsl::Statistics::Num32.
### wabsdev-m(@w!, @data!, Num() $wmean!, Int() :$wstride? = 1, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Num)
This function computes the absolute deviation of the weighted dataset @data about the given weighted mean $wmean. This function is available only for Numeric types, so only when using Math::Libgsl::Statistics or Math::Libgsl::Statistics::Num32.
### wskew(@w!, @data!, Int() :$wstride? = 1, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Num)
This function computes the weighted skewness of the dataset @data. This function is available only for Numeric types, so only when using Math::Libgsl::Statistics or Math::Libgsl::Statistics::Num32.
### wskew-m-sd(@w!, @data!, Num() $wmean!, Num() $wsd!, Int() :$wstride? = 1, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Num)
This function computes the weighted skewness of the dataset @data using the given values of the weighted mean and weighted standard deviation, $wmean and $wsd. This function is available only for Numeric types, so only when using Math::Libgsl::Statistics or Math::Libgsl::Statistics::Num32.
### wkurtosis(@w!, @data!, Int() :$wstride? = 1, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Num)
This function computes the weighted kurtosis of the dataset @data. This function is available only for Numeric types, so only when using Math::Libgsl::Statistics or Math::Libgsl::Statistics::Num32.
### wkurtosis-m-sd(@w!, @data!, Num() $wmean!, Num() $wsd!, Int() :$wstride? = 1, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Num)
This function computes the weighted kurtosis of the dataset @data using the given values of the weighted mean and weighted standard deviation, $wmean and $wsd. This function is available only for Numeric types, so only when using Math::Libgsl::Statistics or Math::Libgsl::Statistics::Num32.
### smax(@data!, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Num)
This function returns the maximum value in @data.
### smin(@data!, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Num)
This function returns the minimum value in @data.
### sminmax(@data!, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> List)
This function returns both the minimum and maximum values in @data in a single pass.
### smax-index(@data!, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Int)
This function returns the index of the maximum value in @data.
### smin-index(@data!, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Int)
This function returns the index of the minimum value in @data.
### sminmax-index(@data!, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> List)
This function returns the indexes of the minimum and maximum values in @data in a single pass.
### median-from-sorted-data(@sorted-data! where { [<] @sorted-data }, Int() :$stride? = 1, Int() :$n? = (@sorted-data.elems / $stride).Int --> Num)
This function returns the median value of @sorted-data.
### median(@data!, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Num)
This function returns the median value of @data.
### quantile-from-sorted-data(@sorted-data! where { [<] @sorted-data }, Num() $percentile!, Int() :$stride? = 1, Int() :$n? = (@sorted-data.elems / $stride).Int --> Num)
This function returns a quantile value of @sorted-data. The quantile is determined by the $percentile, a fraction between 0 and 1. For example, to compute the value of the 75th percentile $percentile should have the value 0.75.
### select(@data!, Int() $k, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Num)
This function finds the k-th smallest element of the input array @data.
### trmean-from-sorted-data(Num() $alpha, @sorted-data! where { [<] @sorted-data }, Int() :$stride? = 1, Int() :$n? = (@sorted-data.elems / $stride).Int --> Num)
This function returns the trimmed mean of @sorted-data.
### gastwirth-from-sorted-data(@sorted-data! where { [<] @sorted-data }, Int() :$stride? = 1, Int() :$n? = (@sorted-data.elems / $stride).Int --> Num)
This function returns the Gastwirth location estimator of @sorted-data.
### mad0(@data!, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Num)
### mad(@data!, Int() :$stride? = 1, Int() :$n? = (@data.elems / $stride).Int --> Num)
These functions return the median absolute deviation of @data. The mad0 function calculates the MAD statistic without the bias correction scale factor.
### Sn0-from-sorted-data(@sorted-data! where { [<] @sorted-data }, Int() :$stride? = 1, Int() :$n? = (@sorted-data.elems / $stride).Int --> Num)
### Sn-from-sorted-data(@sorted-data! where { [<] @sorted-data }, Int() :$stride? = 1, Int() :$n? = (@sorted-data.elems / $stride).Int --> Num)
These functions return the Sₙ statistic of @sorted-data. The Sn0 function calculates the Sₙ statistic without the bias correction scale factors.
### Qn0-from-sorted-data(@sorted-data! where { [<] @sorted-data }, Int() :$stride? = 1, Int() :$n? = (@sorted-data.elems / $stride).Int --> Num)
### Qn-from-sorted-data(@sorted-data! where { [<] @sorted-data }, Int() :$stride? = 1, Int() :$n? = (@sorted-data.elems / $stride).Int --> Num)
These functions return the Qₙ statistic of @sorted-data. The Qn0 function calculates the Qₙ statistic without the bias correction scale factors.
C Library Documentation
=======================
For more details on libgsl see [https://www.gnu.org/software/gsl/](https://www.gnu.org/software/gsl/). The excellent C Library manual is available here [https://www.gnu.org/software/gsl/doc/html/index.html](https://www.gnu.org/software/gsl/doc/html/index.html), or here [https://www.gnu.org/software/gsl/doc/latex/gsl-ref.pdf](https://www.gnu.org/software/gsl/doc/latex/gsl-ref.pdf) in PDF format.
Prerequisites
=============
This module requires the libgsl library to be installed. Please follow the instructions below based on your platform:
Debian Linux and Ubuntu 20.04+
------------------------------
sudo apt install libgsl23 libgsl-dev libgslcblas0
That command will install libgslcblas0 as well, since it's used by the GSL.
Ubuntu 18.04
------------
libgsl23 and libgslcblas0 have a missing symbol on Ubuntu 18.04. I solved the issue installing the Debian Buster version of those three libraries:
* [http://http.us.debian.org/debian/pool/main/g/gsl/libgslcblas0_2.5+dfsg-6_amd64.deb](http://http.us.debian.org/debian/pool/main/g/gsl/libgslcblas0_2.5+dfsg-6_amd64.deb)
* [http://http.us.debian.org/debian/pool/main/g/gsl/libgsl23_2.5+dfsg-6_amd64.deb](http://http.us.debian.org/debian/pool/main/g/gsl/libgsl23_2.5+dfsg-6_amd64.deb)
* [http://http.us.debian.org/debian/pool/main/g/gsl/libgsl-dev_2.5+dfsg-6_amd64.deb](http://http.us.debian.org/debian/pool/main/g/gsl/libgsl-dev_2.5+dfsg-6_amd64.deb)
Installation
============
To install it using zef (a module management tool):
$ zef install Math::Libgsl::Statistics
AUTHOR
======
Fernando Santagata <na[email protected]>
COPYRIGHT AND LICENSE
=====================
Copyright 2020 Fernando Santagata
This library is free software; you can redistribute it and/or modify it under the Artistic License 2.0.