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:

Code Quality Rank: L5
Monthly Downloads: 45,140
Programming language: Ruby
License: GNU General Public License v3.0 or later
Tags: Scientific     SciRuby     Projects    
Latest version: v0.7.0

distribution alternatives and similar gems

Based on the "SciRuby" category.
Alternatively, view distribution alternatives based on common mentions on social networks and blogs.

Do you think we are missing an alternative of distribution or a related project?

Add another 'SciRuby' Gem



Build Status Code Climate

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
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


$ 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


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

API Structure


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


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


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.


  • 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.


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


  • Implementing everything in the distributions x functions table above.


  • 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.