Landau distribution

Landau distribution

Probability density function ${\displaystyle \mu =0,\;c=\pi /2}$
Parameters	${\displaystyle c\in (0,\infty )}$ — scale parameter ${\displaystyle \mu \in (-\infty ,\infty )}$ — location parameter
Support	${\displaystyle \mathbb {R} }$
PDF	${\displaystyle {\frac {1}{\pi c}}\int _{0}^{\infty }e^{-t}\cos \left(t\left({\frac {x-\mu }{c}}\right)+{\frac {2t}{\pi }}\log \left({\frac {t}{c}}\right)\right)\,dt}$
Mean	Undefined
Variance	Undefined
MGF	Undefined
CF	${\displaystyle \exp \left(it\mu -{\frac {2ict}{\pi }}\log |t|-c|t|\right)}$

In probability theory, the Landau distribution^[1] is a probability distribution named after Lev Landau. Because of the distribution's "fat" tail, the moments of the distribution, such as mean or variance, are undefined. The distribution is a particular case of stable distribution.