6 papers · 2 filters
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…
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…
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…
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…
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)΅
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…