20.8 The Exponential Power Distribution

Function: double gsl_ran_exppow (const gsl_rng * r, double a, double b)

This function returns a random variate from the 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 >= 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.

Function: double gsl_ran_exppow_pdf (double x, double a, double 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.

Function: double gsl_cdf_exppow_P (double x, double a, double b)

Function: double gsl_cdf_exppow_Q (double x, double a, double b)

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