The Exponential Power Distribution

gsl_ran_exppow(a, b)

This function returns a random variate from exponential power distribution with scale parameter a and exponent b. The distribution is,

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

for \(x \geq 0\). For \(b = 1\) this reduces to the Laplace distribution. For \(b = 2\) it has the same form as a Gaussian distribution, but with \(a = \sqrt{2} \sigma\).

gsl_ran_exppow_pdf(x, a, b)

This function computes the probability density \(p(x)\) at \(x\) for an exponential power distribution with scale parameter a and exponent b, using the formula given above.

gsl_ran_exppow_P(x, a, b)
gsl_ran_exppow_Q(x, a, b)

These functions compute the cumulative distribution functions \(P(x), Q(x)\) for the exponential power distribution with parameters a and b.