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ABSTRACT This note consists of two parts . In the first part, we provide a pedagogic review on the multivariate generalized hyperbolic (MGH) distribution. We show that this probability family… Click to show full abstract
ABSTRACT This note consists of two parts . In the first part, we provide a pedagogic review on the multivariate generalized hyperbolic (MGH) distribution. We show that this probability family is close under margining, conditioning, and linear transforms; however, such property does not hold for its subclasses. In the second part, we obtain the Stein-type inequality in the context of MGH distribution. Moreover, we apply the Stein-type inequality to prove a lower bound for Var[h(X)]. Particularly, we present examples when X belongs to some well-known subclasses in MGH family.
Journal Title: Communications in Statistics - Theory and Methods
Year Published: 2018
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