Exponential power distribution

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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 2 a \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.

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