Gaussian density kernel
= Gaussian density kernel
{c}
{title2=$K_N(u)=(2\pi)^{-1/2}e^{-u^2/2}$}
The Gaussian density kernel is the standard <normal probability density> used as a unit-integral <kernel for density estimation>. Its second moment is one and $R(K_N)=1/(2\sqrt\pi)$. Its <canonical kernel> has scale $(2\sqrt\pi)^{-1/5}$. It is a function of one smoothing displacement, distinct from the two-argument <Gaussian kernel> used as a <positive-semidefinite kernel>.