Dear all

I’m announcing the availability of QuadraticFormsMGHyp.jl. The purpose of the package is to compute tail probabilities and partial moments of

L\equiv a_0+\mathbf{a}^{\mathrm{\scriptscriptstyle T}}X+X^{\mathrm{\scriptscriptstyle T}}\mathbf{A}X,

where X\sim \mathrm{MGHyp}(\boldsymbol{\mu},\mathbf{C},\boldsymbol{\gamma},\lambda,\chi,\psi); i.e., X has a d-variate generalized hyperbolic distribution with stochastic representation

X=\boldsymbol{\mu}+Y \boldsymbol{\gamma} +\surd{Y}\mathbf{C}Z,

where Z has a d-variate standard Normal distribution, \boldsymbol{\mu} and \boldsymbol{\gamma} are constant d-vectors, \mathbf{C} is a d\times d matrix, and Y has a univariate generalized inverse Gaussian distribution with density

f_{GIG}(y;\lambda,\chi,\psi)\propto y^{\lambda-1}\exp\left\{-\frac{1}{2}\left(\chi y^{-1}+\psi y\right)\right\}.

The generalized hyperbolic distribution contains as special cases, among others, the Variance-Gamma (\lambda>0), Student’s t (\lambda=-\nu/2, \chi=\nu, \psi=0), Normal Inverse Gaussian (\lambda=-1/2), and Hyperbolic (\lambda=1) distributions.

The package provides exact calculations and saddlepoint approximations. The algorithms are from our paper and generalize those of Imhof (Biometrika, 1961) and Broda (Mathematical Finance, 2012).

Cheers
Simon

7 Likes

Thanks this package. Looks really cool!
Have you considered adding it (or a subset) to Distributions.jl at some point?
An advantage of it being part of a larger (well maintained) organization is that if the original developer stops updating it (or gets hit by a bus) it is still likely to be available to more potential users…

2 Likes

Thanks! I’m not sure it’s a good fit with what Distributions.jl is aiming to do. I’ll think about it 