Epanechnikov distribution

Epanechnikov

Parameters	${\displaystyle c>0}$ scale (real)
Support	${\displaystyle -c\leq x\leq c}$
PDF	${\displaystyle {\frac {3}{4c}}\max \left(0,1-\left({\frac {x}{c}}\right)^{2}\right)}$
CDF	${\displaystyle {\frac {1}{2}}+{\frac {3x}{4c}}-{\frac {x^{3}}{4c^{3}}}}$ for ${\displaystyle -c\leq x\leq c}$
Mean	${\displaystyle 0}$
Median	${\displaystyle 0}$
Mode	${\displaystyle 0}$
Variance	${\displaystyle {\frac {c^{2}}{5}}}$

In probability theory and statistics, the Epanechnikov distribution, also known as the Epanechnikov kernel, is a continuous probability distribution that is defined on a finite interval. It is named after V. A. Epanechnikov, who introduced it in 1969 in the context of kernel density estimation.^[1]