distributions

Base Class

Name	Description
BaseDistribution	Bare-bones class for statistical distributions to provide consistent methods.

Derived Distributions

Name	Description	PDF function
ArcSineDistribution	ArcSine distribution.	\(\dfrac{1}{\pi\sqrt{x(1-x)}}\)
BetaDistribution	Beta distribution.	\(\dfrac{1}{B(\alpha,\beta)}x^{\alpha-1}(1-x)^{\beta-1}\)
ChiSquareDistribution	ChiSquare distribution.	\(\dfrac{1}{2^{k/2}\Gamma(k/2)}x^{\frac{k}{2}-1}\exp\left[-\dfrac{x}{2}\right]\)
ExponentialDistribution	Exponential distribution.	\(\lambda\exp\left[-\lambda x\right]\)
FoldedNormalDistribution	Folded Normal distribution.	\(\dfrac{1}{\sqrt{2\pi}\sigma}\exp\left[-\dfrac{(x-\mu)^2}{2\sigma^2}\right] + \dfrac{1}{\sqrt{2\pi}\sigma}\exp\left[-\dfrac{(x+\mu)^2}{2\sigma^2}\right]\)
GammaDistributionSS	Gamma distribution with shape-scale parameterization.	\(\dfrac{1}{\Gamma(\alpha)\theta^\alpha}x^{\alpha - 1}\exp\left[-\dfrac{x}{\theta}\right]\)
GammaDistributionSR	Gamma distribution with shape-rate parameterization.	\(\dfrac{1}{\Gamma(\alpha)}\lambda^\alpha x^{\alpha - 1}\exp\left[-\lambda x\right]\)
GaussianDistribution	Gaussian distribution.	\(\dfrac{1}{\sqrt{2\pi}\sigma}\exp\left[-\dfrac{(x-\mu)^2}{2\sigma^2}\right]\)
HalfNormalDistribution	Half-Normal distribution.	\(\dfrac{1}{\sigma}\sqrt{\dfrac{2}{\pi}}\exp\left[-\dfrac{x^2}{2\sigma^2}\right]\)
LaplaceDistribution	Laplace distribution.	\(\dfrac{1}{2b}\exp\left[-\dfrac{|x-\mu|}{b}\right]\)
LogNormalDistribution	Log-Normal distribution.	\(\dfrac{1}{x\sigma\sqrt{2\pi}}\exp\left[-\dfrac{(\ln x-\mu)^2}{2\sigma^2}\right]\)
SkewNormalDistribution	Skew-Normal distribution.	\(\dfrac{2}{\sigma}\phi\left[\dfrac{x-\mu}{\sigma}\right]\Phi\left[\alpha\left(\dfrac{x-\mu}{\sigma}\right)\right]\)
UniformDistribution	Uniform distribution.	\(\dfrac{1}{b-a}\ \forall\ x\in[a,b]\ \text{else}\ 0\)

Other functions

Name	Description
line()	Line function.
linear()	Similar to line().
quadratic()	Quadratic function
cubic()	Cubic function
nth_polynomial()	Polynomial function