# Distribution

## Installation

``````\$ gem install distribution
``````

If you have GSL installed and want to speed things up, install `rb-gsl`:

``````\$ gem install rb-gsl
``````

## Description

Statistical Distributions library. Includes Normal univariate and bivariate, T, F, Chi Square, Binomial, Hypergeometric, Exponential, Poisson, Beta, LogNormal and Gamma.

Uses Ruby by default and C (statistics2/GSL) or Java extensions where available.

Includes code from statistics2 on Normal, T, F and Chi Square ruby code [http://blade.nagaokaut.ac.jp/~sinara/ruby/math/statistics2]

## Synopsis

• Returns Gaussian PDF for x
``````pdf=Distribution::Normal.pdf(x)
``````
• Returns Gaussian CDF for x
``````cdf=Distribution::Normal.cdf(x)
``````
• Returns inverse CDF (or p-value) for x
``````pv=Distribution::Normal.p_value(x)
``````

## Developers

``````\$ git clone https://github.com/SciRuby/distribution.git
``````

If you want to provide a new distribution, run `lib/distribution`:

``````\$ distribution --new your_distribution
``````

This should create the main distribution file, the directory with Ruby and GSL engines and specs on the spec/ directory.

## API Structure

Distribution::.(cdf|pdf|p_value|rng)

On discrete distributions, exact Ruby implementations of pdf, cdf and p_value could be provided, using

``````  Distribution::<name>.exact_(cdf|pdf|p_value)
``````

module Distribution::Shorthand provides (you guess?) shortands method to call all methods

``````  <Distribution shortname>_(cdf|pdf|p|r)
``````

On discrete distributions, exact cdf, pdf and p_value are

``````  <Distribution shortname>_(ecdf|epdf|ep)
``````

Shortnames for distributions:

• Normal: norm
• Bivariate Normal: bnor
• T: tdist
• F: fdist
• Chi Square: chisq
• Binomial: bino
• Hypergeometric: hypg
• Exponential: expo
• Poisson: pois
• Beta: beta
• Gamma: gamma
• LogNormal: lognormal

### API Structure Example

``````  Distribution::T.cdf
``````

could be called after including Distribution::Shorthand

``````  tdist_cdf
``````

## Features

• Very fast ruby 1.8.7/1.9.+ implementation, with improved method to calculate factorials and others common functions
• All methods tested on several ranges. See spec/

## Issues

• On JRuby and Rubinius, BivariateNormal returns incorrect pdf

For current issues see the issue tracker pages.