## 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.
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.
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.
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).
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.
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).