arXiv subjects

Heather L. Sutcliffe

Publications and source records attributed to Heather L. Sutcliffe.

4 recordsLinked to original sources

arXiv2026

The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions

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 integral representations of the density presented. These formulas are then applied to obtain asymptotic expansions for the probability density function, tail probabilities and quantile functions of these distributions. As a special case, we deduce asymptotic expansions for the probability density function of the product of correlated normal random variables with the coefficients given in closed-form. Numerical results are presented to assess the accuracy of our asymptotic approximations across a range of parameter constellations.

math.PR↗

arXiv2026

The distribution of the ratio of products of independent zero mean normal random variables

Let $X_1,\ldots,X_M$ and $Y_1,\ldots,Y_N$ be independent zero mean normal random variables with variances $σ_{X_i}^2$, $i=1,\ldots,M$, and $σ_{Y_j}^2$, $j=1,\ldots,N$, respectively, and let $X=X_1\cdots X_M$ and $Y=Y_1\cdots Y_N$. In this paper, we derive the exact probability density function of the ratio $X/Y$. We apply this formula to derive exact formulas for the cumulative distribution function and the characteristic function. We also obtain further distributional properties, including asymptotic approximations for the probability density function, tail probabilities and the quantile function.

math.PR↗

arXiv2025

Stein's method for asymmetric Laplace approximation

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 asymmetric Laplace distribution. Our results generalise and offer technical refinements on existing results concerning Stein's method for (symmetric) Laplace approximation. We provide general bounds for asymmetric Laplace approximation in the Kolmogorov and Wasserstein distances, and a smooth Wasserstein distance, that involve a distributional transformation that can be viewed as an asymmetric Laplace analogue of the zero bias transformation. As an application, we derive explicit Kolmogorov, Wasserstein and smooth Wasserstein distance bounds for the asymmetric Laplace approximation of geometric random sums, and complement these results by providing explicit bounds for the asymmetric Laplace approximation of a deterministic sum of random variables with a random normalisation sequence.

math.PR↗

arXiv2024

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

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 of independent copies of such random variables. Our Stein characterisation is shown to naturally generalise a number of other Stein characterisations in the literature. From our Stein characterisation we derive recursive formulas for the moments of the product of two correlated normal random variables, and more generally the sum of independent copies of such random variables, which allows for efficient computation of higher order moments.

math.PR↗