Exponential power distribution

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

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

For b = 1 this reduces to the Laplace distribution. For b = 2 it is a normal distribution with $\scriptstyle a\,=\,{\sqrt {2}}\sigma$.