Generalized hyperbolic distribution

This implementation uses the same parametrization as scipy.stats.genhyperbolic in SciPy. The parametrization used here is a true location/scale family. This is not the same as, for example, the parametrization used in the wikipedia article https://en.wikipedia.org/wiki/Generalised_hyperbolic_distribution.

A disadvantage of this parametrization is that, because the parameter δ has been “scaled away”, the variance gamma distribution cannot be obtained as a special case of this distribution. In the parametrization used in the wikipedia article, the variance gamma distribution is obtained by setting δ = 0.

mpsci.distributions.genhyperbolic.cdf(x, p, a, b, loc=0, scale=1)

Cumulative distribution function of the generalized hyperbolic distr.

The result is computed by numerically integrating the PDF, so it is relatively slow.

mpsci.distributions.genhyperbolic.logpdf(x, p, a, b, loc=0, scale=1)

Logarithm of the PDF of the generalized hyperbolic distribution.

mpsci.distributions.genhyperbolic.mean(p, a, b, loc=0, scale=1)

Mean of the generalized hyperbolic distribution.

mpsci.distributions.genhyperbolic.pdf(x, p, a, b, loc=0, scale=1)

Probability density function of the generalized hyperbolic distribution.

mpsci.distributions.genhyperbolic.support(p, a, b, loc=0, scale=1)

Support of the generalized hyperbolic distribution.

mpsci.distributions.genhyperbolic.var(p, a, b, loc=0, scale=1)

Variance of the generalized hyperbolic distribution.