distributions#
Base Class#
Name |
Description |
|---|---|
Bare-bones class for statistical distributions to provide consistent methods. |
Derived Distributions#
Name |
Description |
PDF function |
|---|---|---|
ArcSine distribution. |
\(\dfrac{1}{\pi\sqrt{x(1-x)}}\) |
|
Beta distribution. |
\(\dfrac{1}{B(\alpha,\beta)}x^{\alpha-1}(1-x)^{\beta-1}\) |
|
ChiSquare distribution. |
\(\dfrac{1}{2^{k/2}\Gamma(k/2)}x^{\frac{k}{2}-1}\exp\left[-\dfrac{x}{2}\right]\) |
|
Exponential distribution. |
\(\lambda\exp\left[-\lambda x\right]\) |
|
Folded Normal distribution. |
\(\dfrac{1}{\sqrt{2\pi}\sigma}\exp\left[-\dfrac{(x-\mu)^2}{2\sigma^2}\right] + \dfrac{1}{\sqrt{2\pi}\sigma}\exp\left[-\dfrac{(x+\mu)^2}{2\sigma^2}\right]\) |
|
Gamma distribution. |
\(\dfrac{1}{\Gamma(\alpha)\theta^\alpha}x^{\alpha - 1}\exp\left[-\dfrac{x}{\theta}\right]\) |
|
Gaussian distribution. |
\(\dfrac{1}{\sqrt{2\pi}\sigma}\exp\left[-\dfrac{(x-\mu)^2}{2\sigma^2}\right]\) |
|
Half-Normal distribution. |
\(\dfrac{1}{\sigma}\sqrt{\dfrac{2}{\pi}}\exp\left[-\dfrac{x^2}{2\sigma^2}\right]\) |
|
Laplace distribution. |
\(\dfrac{1}{2b}\exp\left[-\dfrac{|x-\mu|}{b}\right]\) |
|
Log-Normal distribution. |
\(\dfrac{1}{x\sigma\sqrt{2\pi}}\exp\left[-\dfrac{(\ln x-\mu)^2}{2\sigma^2}\right]\) |
|
Scaled inverse chi-squared distribution. |
\(\dfrac{\tau^2(\nu/2)}{\Gamma(\nu/2)}\dfrac{1}{x^{1+(\nu/2)}}\exp\left[-\dfrac{\nu\tau^2}{2x}\right]\) |
|
Skew-Normal distribution. |
\(\dfrac{2}{\sigma}\phi\left[\dfrac{x-\mu}{\sigma}\right]\Phi\left[\alpha\left(\dfrac{x-\mu}{\sigma}\right)\right]\) |
|
Symmetric generalized Normal distribution. |
\(\dfrac{\beta}{2\Gamma(1/\beta)}\exp\left(-\left|\dfrac{x - \mu}{\alpha}\right|^\beta\right)\) |
|
Uniform distribution. |
\(\dfrac{1}{b-a}\ \forall\ x\in[a,b]\ \text{else}\ 0\) |
Non-distribution function#
Name |
Description |
Function |
|---|---|---|
First order polynomial. |
\(mx+c\) |
|
Quadratic polynomial. |
\(ax^2+bx+c\) |
|
Cubic polynomial. |
\(ax^3+bx^2+cx+d\) |