# 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.