activity
20242026
collaborators
Showing 2024 · math.PRShow all

6 papers · 2 filters

math.PR2024

On Stein factors in Stein's method for normal approximation

Robert E. Gaunt

Building on the rather large literature concerning the regularity of the solution of the standard normal Stein equation, we provide a complete description of the best possible unif…

math.PR2024

Asymptotic approximations for the distribution of the product of correlated normal random variables

Robert E. Gaunt, Zixin Ye

We obtain asymptotic approximations for the probability density function of the product of two correlated normal random variables with non-zero means and arbitrary variances. As a…

math.PR2024

A Stein characterisation of the distribution of the product of correlated normal random variables

Robert E. Gaunt, Siqi Li, Heather L. Sutcliffe

We obtain a Stein characterisation of the distribution of the product of two correlated normal random variables with non-zero means, and more generally the distribution of the sum…

math.PR2024

Absolute moments of the variance-gamma distribution

Robert E. Gaunt

We obtain exact formulas for the absolute raw and central moments of the variance-gamma distribution, as infinite series involving the modified Bessel function of the second kind a…

math.PR2024

A probabilistic proof of some integral formulas involving incomplete gamma functions

Robert E. Gaunt

The theory of normal variance mixture distributions is used to provide elementary derivations of closed-form expressions for the definite integrals $\int_0^\infty x^{-2ν}\cos(bx)΅

math.PR2024

The distribution of the product of independent variance-gamma random variables

Robert E. Gaunt, Siqi Li

Let and be independent variance-gamma random variables with zero location parameter; then the exact probability density function of the product is derived. Some basic…