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A Stein characterisation of the generalized hyperbolic distribution

Robert E. Gaunt
2017 E S A I M: Probability & Statistics  
The generalized hyperbolic (GH) distributions form a five parameter family of probability distributions that includes many standard distributions as special or limiting cases, such as the generalized inverse Gaussian distribution, Student's tdistribution and the variance-gamma distribution, and thus the normal, gamma and Laplace distributions. In this paper, we consider the GH distribution in the context of Stein's method. In particular, we obtain a Stein characterisation of the GH distribution
more » ... the GH distribution that leads to a Stein equation for the GH distribution. This Stein equation reduces to the Stein equations from the current literature for the aforementioned distributions that arise as limiting cases of the GH superclass.
doi:10.1051/ps/2017007 fatcat:u2gzvs6nmrcl7jqnwo7afgyoou