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 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109  GNU Scientific Library – Reference Manual: The Exponential Power Distribution

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.