Related papers: Linear combination of bilateral gamma random varia…
This paper deals with bilateral-gamma (BG) approximation to functionals of an isonormal Gaussian process. We use Malliavin-Stein method to obtain the error bounds for the smooth Wasserstein distance. As by-products, the error bounds for…
The variance-gamma (VG) distributions form a four parameter family that includes as special and limiting cases the normal, gamma and Laplace distributions. Some of the numerous applications include financial modelling and approximation on…
In this article we introduce a three-parameter extension of the bivariate exponential-geometric (BEG) law (Kozubowski and Panorska, 2005). We refer to this new distribution as bivariate gamma-geometric (BGG) law. A bivariate random vector…
The gamma difference distribution is defined as the difference of two gamma distributions, with in general different shape and rate parameters. Starting with knowledge of the corresponding characteristic function, a second order linear…
In this paper we propose a new, simple and explicit mechanism allowing to derive Stein operators for random variables whose characteristic function satisfies a simple ODE. We apply this to study random variables which can be represented as…
This article compares the distributions of integer-valued random variables and Poisson random variables. It considers the total variation and the Wasserstein distance and provides, in particular, explicit bounds on the pointwise difference…
The variance-gamma (VG) distributions form a four-parameter family which includes as special and limiting cases the normal, gamma and Laplace distributions. Some of the numerous applications include financial modelling and distributional…
We provide a general bound on the Wasserstein distance between two arbitrary distributions of sequences of Bernoulli random variables. The bound is in terms of a mixing quantity for the Glauber dynamics of one of the sequences, and a simple…
We combine the method of exchangeable pairs with Stein's method for functional approximation. As a result, we give a general linearity condition under which an abstract Gaussian approximation theorem for stochastic processes holds. We apply…
We develop a new formulation of Stein's method to obtain computable upper bounds on the total variation distance between the geometric distribution and a distribution of interest. Our framework reduces the problem to the construction of a…
In this paper, we extend Stein's method to products of independent beta, gamma, generalised gamma and mean zero normal random variables. In particular, we obtain Stein operators for mixed products of these distributions, which include the…
We introduce and document a class of probability distributions, called bilateral generalized inverse Gaussian (BGIG) distributions, that are obtained by convolution of two generalized inverse Gaussian distributions supported by the positive…
In this article, we first obtain, for the Kolmogorov distance, an error bound between a tempered stable and a compound Poisson distribution and also an error bound between a tempered stable and an alpha stable distribution via Stein method.…
Let F ($\nu$) be the centered Gamma law with parameter $\nu$ > 0 and let us denote by P Y the probability distribution of a random vector Y. We develop a multidimensional variant of the Stein's method for Gamma approximation that allows to…
We consider the number of crossings in a random embedding of a graph, $G$, with vertices in convex position. We give explicit formulas for the mean and variance of the number of crossings as a function of various subgraph counts of $G$.…
The geometric sum plays a significant role in risk theory and reliability theory \cite{Kala97} and a prototypical example of the geometric sum is R\'enyi's theorem~\cite{Renyi56} saying a sequence of suitably parameterised geometric sums…
Variance-Gamma distributions are widely used in financial modelling and contain as special cases the normal, Gamma and Laplace distributions. In this paper we extend Stein's method to this class of distributions. In particular, we obtain a…
The product of two zero mean correlated normal random variables, and more generally the sum of independent copies of such random variables, has received much attention in the statistics literature and appears in many application areas.…
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…
In this paper, we study some aspects on random analysis on the L\'eevy stochastic processes with margins following generalized hyperbolic distributions generated by gamma laws. In particular we study the boundedness of its total variations…