Distribution of RV X

Symbolic

Representation

Significance of Parameters

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normal or Gaussian

$N\left(\mu ,{\sigma }^2\right)$

$\begin{array}{l}\mu =\text{meanof}X\\ \sigma =\text{standarddeviationof}X\end{array}$

$\frac{1}{\sqrt{2\text{π}}\sigma }\exp \left(-\frac{{\left(x-\mu \right)}^2}{2{\sigma }^2}\right)$

log-normal

$\Lambda \left(m,s^2\right)$

$\begin{array}{l}m=\text{meanof}Y=\ln \left(X\right)\\ s=\text{standarddeviationof}Y\end{array}$

$\frac{1}{\sqrt{2\text{π}}\sigma x}\exp \left(-\frac{{\left(\ln \left(x\right)-\mu \right)}^2}{2{\sigma }^2}\right)$

uniform

$U\left(a,b\right)$

$\begin{array}{l}a=\text{lowerboundary}\\ b=\text{upperboundary}\end{array}$

$\frac{1}{b-a}\left[H\left(x-a\right)-H\left(x-b\right)\right]$

Laplace

$La\left(\mu ,\beta \right)$

$\begin{array}{l}\mu =\text{locationparameter}\\ \beta =\text{scaleparameter}\end{array}$

$\frac{1}{2\beta }\exp \left(-\frac{\left|x-\mu \right|}{\beta }\right)$