6 papers · 2 filters
On the product of correlated normal random variables and the noncentral chi-square difference distribution
Robert E. Gaunt
We represent the product of two correlated normal random variables, and more generally the sum of independent copies of such random variables, as a difference of two independent no…
Stein's method for asymmetric Laplace approximation
Fraser Daly, Robert E. Gaunt, Heather L. Sutcliffe
Motivated by its appearance as a limiting distribution for random and non-random sums of independent random variables, in this paper we develop Stein's method for approximation by…
The variance-gamma product distribution
Robert E. Gaunt, Siqi Li, Heather Sutcliffe
We derive the exact probability density function of the product of independent variance-gamma random variables with zero location parameter. We then apply this formula to deriv…
Infinite Divisibility of the Product of Two Correlated Normal Random Variables and Exact Distribution of the Sample Mean
Robert E. Gaunt, Saralees Nadarajah, Tibor K. Pogány
We prove that the distribution of the product of two correlated normal random variables with arbitrary means and arbitrary variances is infinitely divisible. We also obtain exact f…
Asymptotic expansions relating to the distribution of the product of correlated normal random variables
Robert E. Gaunt, Zixin Ye
Asymptotic expansions are derived for the tail distribution of the product of two correlated normal random variables with non-zero means and arbitrary variances, and more generally…
Polynomial Stein operators: a noncommutative algebra perspective
Ehsan Azmoodeh, Dario Gasbarra, Robert E. Gaunt
In this paper, we make a novel connection between Stein's method and noncommutative algebra by viewing polynomial Stein operators (Stein operators with polynomial coefficients) as…