# openmc.stats – Statistics¶

## Univariate Probability Distributions¶

 openmc.stats.Univariate Probability distribution of a single random variable. openmc.stats.Discrete Distribution characterized by a probability mass function. openmc.stats.Uniform Distribution with constant probability over a finite interval [a,b] openmc.stats.Maxwell Maxwellian distribution in energy. openmc.stats.Watt Watt fission energy spectrum. openmc.stats.Tabular Piecewise continuous probability distribution. openmc.stats.Legendre Probability density given by a Legendre polynomial expansion $$\sum\limits_{\ell=0}^N \frac{2\ell + 1}{2} a_\ell P_\ell(\mu)$$. openmc.stats.Mixture Probability distribution characterized by a mixture of random variables. openmc.stats.Normal Normally distributed sampling. openmc.stats.Muir Muir energy spectrum.

## Angular Distributions¶

 openmc.stats.UnitSphere Distribution of points on the unit sphere. openmc.stats.PolarAzimuthal Angular distribution represented by polar and azimuthal angles openmc.stats.Isotropic Isotropic angular distribution. openmc.stats.Monodirectional Monodirectional angular distribution.

## Spatial Distributions¶

 openmc.stats.Spatial Distribution of locations in three-dimensional Euclidean space. openmc.stats.CartesianIndependent Spatial distribution with independent x, y, and z distributions. openmc.stats.Box Uniform distribution of coordinates in a rectangular cuboid. openmc.stats.Point Delta function in three dimensions.