[ANN] New package QuadraticFormsMGHyp

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).



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…


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