## Uses of Interfacecom.opengamma.strata.math.impl.statistics.distribution.ProbabilityDistribution

• Packages that use ProbabilityDistribution
Package Description
com.opengamma.strata.math.impl.statistics.distribution
• ### Uses of ProbabilityDistribution in com.opengamma.strata.math.impl.statistics.distribution

Classes in com.opengamma.strata.math.impl.statistics.distribution that implement ProbabilityDistribution
Modifier and Type Class Description
class  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 $y$.
class  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.
class  GammaDistribution
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.
class  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.
class  GeneralizedParetoDistribution
Calculates the Pareto distribution.
class  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.
class  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).
class  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.
class  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).