16 papers · 1 filter
On Pólya's 4D random walk constant
Robert E. Gaunt
The return probability in the simple symmetric random walk on the 4-dimensional lattice is evaluated in closed form in terms of the generalized hypergeometric functi…
Log-convexity and log-concavity of noncentral gamma sums and differences
Robert E. Gaunt, Frédéric Ouimet
We study log-convexity and log-concavity of densities obtained from sums and differences of two independent noncentral gamma random variables. We give a complete classification of…
On Wilks' problem: Exact recursive formulas via Stein's method for the joint moments of disjoint principal minors of Wishart random matrices
Robert E. Gaunt, Frédéric Ouimet
In a 1934 Annals of Mathematics paper, Samuel S. Wilks posed the problem of computing joint moments of disjoint principal minors of Wishart random matrices, describing the general…
Stein's method for the symmetric matrix normal distribution with an application to the approximation of the Wishart law
Robert E. Gaunt, Frédéric Ouimet
In this paper, we extend Stein's method to the symmetric matrix normal distribution. In particular, we obtain a Stein characterization of the symmetric matrix normal distribution i…
Stein's method for the Wishart distribution
Gabriel Bailly, Robert E. Gaunt, Frédéric Ouimet +2
In this work, we develop Stein's method for the Wishart distribution on the cone of positive definite matrices. We establish the basic ingredients of a Wishart Stein framework: we…
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…