# 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 | CDF | Quantile | RNG | Mean | Mode | Variance | Skewness | Kurtosis | Entropy | |
---|---|---|---|---|---|---|---|---|---|---|

Uniform | x | x | x | x | x | x | ||||

Normal | 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 | ||||

Logistic | x | x | x | x | x | x | ||||

Student's T | x | x | x | x | x | x | x | |||

Chi Square | x | x | x | x | x | x | ||||

Fisher-Snedecor | x | x | x | x | x | x | x | |||

Beta | x | x | x | x | x | x | x | |||

Gamma | x | x | x | x | x | x | x | x | ||

Weibull | x | x | x | x | x | x | x | |||

Binomial | x | x | x | x | x | x | x | |||

Poisson | x | x | x | x | x | x | ||||

Hypergeometric | x | x | x | x | x | x | x |

## Installation

```
$ gem install distribution
```

You can install GSL for better performance:

- For Mac OS X:
`brew install gsl`

- For Ubuntu / Debian:
`sudo apt-get install libgsl0-dev`

After successfully installing the library:

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

## Examples

You can find automatically generated documentation on RubyDoc.

```
# 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
- Uniform: unif

## Roadmap

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 Student's t, 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.

### Long-term

- Implementing everything in the distributions x functions table above.

## 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.