Exponential power distribution

The exponential power distribution, also known as the generalized error distribution, takes a scale parameter a and exponent b. The probability density is

$p(x)\mathrm {d} x={1 \over 2a\Gamma (1+1/b)}\exp {(-|x/a|^{b})}\mathrm {d} x$

For b = 1 this reduces to the Laplace distribution. For b = 2 it has the same form as a Gaussian distribution, but with $a={\sqrt {2}}\sigma$.