5 papers · 1 filter
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…
Stein's method and the distribution of the product of zero mean correlated normal random variables
Robert E. Gaunt
Over the last 80 years there has been much interest in the problem of finding an explicit formula for the probability density function of two zero mean correlated normal random var…
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…