# Distribution

Distribution is a gem with several probabilistic distributions. Pure Ruby is used by default, C (GSL) or Java extensions are used if available. Some facts:

• Very fast ruby 1.9.3+ implementation, with improved method to calculate factorials and other common functions.
• All methods tested on several ranges. See `spec/`.
• Code for normal, Student's t and chi square is lifted from the statistics2 gem. Originally at this site.
• The code for some functions and RNGs was lifted from Julia's Rmath-julia, a patched version of R's standalone math library.

The following table lists the available distributions and the methods available for each one. If a field is marked with an x, that distribution doesn't have that method implemented.

Distribution PDF CDF Quantile RNG Mean Mode Variance Skewness Kurtosis Entropy
Uniform x x x x x x x x x x
Normal x x x x x x x x x x
Lognormal x x x x x x x x
Bivariate Normal x x x x x x x x
Exponential x x x x x x x x
Logistic x x x x x x x x
t-Student x x x x x x x x
Chi Square x x x x x x x x
Fisher-Snedecor x x x x x x x x
Beta x x x x x x x x
Gamma x x x x x x x x
Weibull x x x x x x x x
Binomial x x x x x x x x
Poisson x x x x x x x x
Hypergeometric x x x x x x x x

## Installation

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

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

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

## Examples

``````# 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)

# API.

# You would normally use the following
p = Distribution::T.cdf(x)

# to get the cumulative probability of `x`. However, you can also:

include Distribution::Shorthand
tdist_cdf(x)
``````

## API Structure

``````Distribution::<name>.(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

This gem wasn't updated for a long time before I started working on it, so there are a lot of work to do. The first priority is cleaning the interface and removing cruft whenever possible. After that, I want to implement more distributions and make sure that each one has a RNG.

### Short-term

• Define a minimal interface for continuous and discrete distributions (e.g. mean, variance, mode, skewness, kurtosis, pdf, cdf, quantile, cquantile).
• Implement `Distribution::Uniform` with the default Ruby `Random`.
• Clean up the implementation of normal distribution. Implement the necessary functions.
• The same for t-student, chi square, Fisher-Snedecor, beta, gamma, lognormal, logistic.
• The same for discrete distributions: binomial, hypergeometric, bernoulli (still missing), etc.

### Medium-term

• Implement DSFMT for the uniform random generator.
• Cauchy distribution.

• ???

## Issues

• On JRuby and Rubinius, BivariateNormal returns incorrect pdf

For current issues see the issue tracker pages.

## OMG! I want to help!

Everyone is welcome to help! Please, test these distributions with your own use cases and give a shout on the issue tracker if you find a problem or something is strange or hard to use. Documentation pull requests are totally welcome. More generally, any ideas or suggestions are welcome -- even by private e-mail.

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.