Generalized Hyperbolic Distribution

The Generalized Hyperbolic Distribution is defined as the normal variance-mean mixture with Generalized Inverse Gaussian distribution as the mixing distribution. The "hyperbolic" characterization refers to the fact that the shape of the log-probability distribution can be described as a hyperbola. Hyperbolic distributions are sometime referred to as semi-fat tailed because their probability density decrease slower than "sub-hyperbolic" distributions (e.g. normal distribution, whose log-probability decreases quadratically), but faster than other "extreme value" distributions (e.g. pareto distribution, whose log-probability decreases logarithmically).

Functions

Different parameterizations exist in the literature; SciPy implements the "4th parametrization" in Prause (1999).