# Random Number Distributions

This chapter describes functions for generating random variates and computing their probability distributions. Samples from the distributions described in this chapter can be obtained using any of the random number generators in the library as an underlying source of randomness. In the simplest cases a non-uniform distribution can be obtained analytically from the uniform distribution of a random number generator by applying an appropriate transformation. This method uses one call to the random number generator.

More complicated distributions are created by the acceptance-rejection method, which compares the desired distribution against a distribution which is similar and known analytically. This usually requires several samples from the generator.

The functions described in this section are declared in ``gsl_randist.h'`.

- The Gaussian Distribution
- The Gaussian Tail Distribution
- The Bivariate Gaussian Distribution
- The Exponential Distribution
- The Laplace Distribution
- The Exponential Power Distribution
- The Cauchy Distribution
- The Rayleigh Distribution
- The Rayleigh Tail Distribution
- The Landau Distribution
- The Levy alpha-Stable Distributions
- The Levy skew alpha-Stable Distribution
- The Gamma Distribution
- The Flat (Uniform) Distribution
- The Lognormal Distribution
- The Chi-squared Distribution
- The F-distribution
- The t-distribution
- The Beta Distribution
- The Logistic Distribution
- The Pareto Distribution
- The Spherical Distribution (2D & 3D)
- The Weibull Distribution
- The Type-1 Gumbel Distribution
- The Type-2 Gumbel Distribution
- The Dirichlet Distribution
- General Discrete Distributions
- The Poisson Distribution
- The Bernoulli Distribution
- The Binomial Distribution
- The Multinomial Distribution
- The Negative Binomial Distribution
- The Pascal Distribution
- The Geometric Distribution
- The Hypergeometric Distribution
- The Logarithmic Distribution
- Shuffling and Sampling
- Random Number Distribution Examples
- Random Number Distribution References and Further Reading