8 papers
Closed-form evaluation of the cumulative distribution function and absolute moments of the variance-gamma distribution
Robert E. Gaunt, Heather L. Sutcliffe
Closed-form formulas are derived for the cumulative distribution function and odd-order absolute moments of the variance-gamma distribution. As a special case, closed-form expressi…
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions
Robert E. Gaunt, Heather L. Sutcliffe
Exact formulas are derived for the probability density functions of the sum and difference of two independent non-central gamma distributed random variables, with both series and i…
The distribution of the ratio of products of independent zero mean normal random variables
Robert E. Gaunt, Heather L. Sutcliffe
Let and be independent zero mean normal random variables with variances , , and , , respectively…
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…
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…
Bounds for distributional approximation in the multivariate delta method by Stein's method
Robert E. Gaunt, Heather Sutcliffe
We obtain bounds to quantify the distributional approximation in the delta method for vector statistics (the sample mean of independent random vectors) for normal and non-norma…
Improved bounds in Stein's method for functions of multivariate normal random vectors
Robert E. Gaunt, Heather Sutcliffe
In a recent paper, Gaunt 2020 extended Stein's method to limit distributions that can be represented as a function of a centered multivariate…