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|Probability density function|
|Cumulative distribution function|
|Parameters|| location (real)|
where is the modified Bessel function of the second kind.
As the name suggests it is of a very general form, being the superclass of, among others, the Student's t-distribution, the hyperbolic distribution and the normal-inverse Gaussian distribution.
Its main areas of application are those which require sufficient probability of far-field behaviour, which it can model due to its semi-heavy tails, a property that the normal distribution does not possess. The generalised hyperbolic distribution is well-used in economics, with particular application in the fields of modelling financial markets and risk management, due to its semi-heavy tails.
- has a Student's t-distribution with degrees of freedom.
- has a hyperbolic distribution.
- has a normal-inverse Gaussian distribution.
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