5 papers
On bounds for the mode and median of the generalized hyperbolic and related distributions
Robert E. Gaunt, Milan Merkle
Except for certain parameter values, a closed form formula for the mode of the generalized hyperbolic (GH) distribution is not available. In this paper, we exploit results from the…
A simple proof of the characteristic function of Student's -distribution
Robert E. Gaunt
This note presents a simple proof of the characteristic function of Student's -distribution. The method of proof, which involves finding a differential equation satisfied by the…
Some new Stein operators for product distributions
Robert E. Gaunt, Guillaume Mijoule, Yvik Swan
We provide a general result for finding Stein operators for the product of two independent random variables whose Stein operators satisfy a certain assumption, extending a recent r…
Inequalities for some integrals involving modified Lommel functions of the first kind
Robert E. Gaunt
In this paper, we obtain inequalities for some integrals involving the modified Lommel function of the first kind . In most cases, these inequalities are tight in certa…
Bounds for modified Lommel functions of the first kind and their ratios
Robert E. Gaunt
The modified Lommel function is an important special function, but to date there has been little progress on the problem of obtaining functional inequalities for $t_{μ…