# Package com.opengamma.strata.math.impl.statistics.distribution

• Interface Summary
Interface Description
ProbabilityDistribution<T>
Interface for probability distributions.
• Class Summary
Class Description
BivariateNormalDistribution
The bivariate normal distribution is a continuous probability distribution of two variables, $x$ and $y$, with cdf \begin{align*} M(x, y, \rho) = \frac{1}{2\pi\sqrt{1 - \rho^2}}\int_{-\infty}^x\int_{-\infty}^{y} e^{\frac{-(X^2 - 2\rho XY + Y^2)}{2(1 - \rho^2)}} dX dY \end{align*} where $\rho$ is the correlation between $x$ and $y$.
ChiSquareDistribution
A $\chi^2$ distribution with $k$ degrees of freedom is the distribution of the sum of squares of $k$ independent standard normal random variables with cdf and inverse cdf \begin{align*} F(x) &=\frac{\gamma\left(\frac{k}{2}, \frac{x}{2}\right)}{\Gamma\left(\frac{k}{2}\right)}\\ F^{-1}(p) &= 2\gamma^{-1}\left(\frac{k}{2}, p\right) \end{align*} where $\gamma(y, z)$ is the lower incomplete Gamma function and $\Gamma(y)$ is the Gamma function.
The Gamma distribution is a continuous probability distribution with cdf \begin{align*} F(x)=\frac{\gamma\left(k, \frac{x}{\theta}\right)}{\Gamma(k)} \end{align*} and pdf \begin{align*} f(x)=\frac{x^{k-1}e^{-\frac{x}{\theta}}}{\Gamma{k}\theta^k} \end{align*} where $k$ is the shape parameter and $\theta$ is the scale parameter.
GeneralizedExtremeValueDistribution
The generalized extreme value distribution is a family of continuous probability distributions that combines the Gumbel (type I), Fréchet (type II) and Weibull (type III) families of distributions.
GeneralizedParetoDistribution
Calculates the Pareto distribution.
LaplaceDistribution
The Laplace distribution is a continuous probability distribution with probability density function \begin{align*} f(x)=\frac{1}{2b}e^{-\frac{|x-\mu|}{b}} \end{align*} where $\mu$ is the location parameter and $b$ is the scale parameter.
NonCentralChiSquaredDistribution
The non-central chi-squared distribution is a continuous probability distribution with probability density function \begin{align*} f_r(x) = \frac{e^-\frac{x + \lambda}{2}x^{\frac{r}{2} - 1}}{2^{\frac{r}{2}}}\sum_{k=0}^\infty \frac{(\lambda k)^k}{2^{2k}k!\Gamma(k + \frac{r}{2})} \end{align*} where $r$ is the number of degrees of freedom, $\lambda$ is the non-centrality parameter and $\Gamma$ is the Gamma function (GammaFunction).
NormalDistribution
The normal distribution is a continuous probability distribution with probability density function \begin{align*} f(x) = \frac{1}{\sqrt{2\pi}\sigma} e^{-\frac{(x - \mu)^2}{2\sigma^2}} \end{align*} where $\mu$ is the mean and $\sigma$ the standard deviation of the distribution.
StudentTDistribution
Student's T-distribution is a continuous probability distribution with probability density function \begin{align*} f(x) = \frac{\Gamma\left(\frac{\nu + 1}{2}\right)}{\sqrt{\nu\pi}\Gamma(\left(\frac{\nu}{2}\right)}\left(1 + \frac{x^2}{\nu}\right)^{-\frac{1}{2}(\nu + 1)} \end{align*} where $\nu$ is the number of degrees of freedom and $\Gamma$ is the Gamma function (GammaFunction).
StudentTOneTailedCriticalValueCalculator
StudentT calculator.
StudentTTwoTailedCriticalValueCalculator
StudentT calculator.