Related papers: Discrete Stein characterizations and discrete info…
Here we introduce some new classes of discrete stable random variables, which are useful for understanding of a new general notion of stability of random variables called us as casual stability. There are given some examples of casual and…
Several characterizations of the Generalized Inverse Gaussian (GIG) distribution have been proposed in the literature, especially over the past two decades. These characterization theorems are surveyed, and two new characterizations are…
We develop a multidimensional Stein methodology for non-degenerate self-decomposable random vectors in $\mathbb{R}^d$ having finite first moment. Building on previous univariate findings, we solve an integro-partial differential Stein…
We investigate the common underlying discrete structures for various smooth and discrete nets. The main idea is to impose the characteristic properties of the nets not only on elementary quadrilaterals but also on larger parameter…
We introduce the discrete distribution of a Wiener process range. Rather than finding some basic distributional properties including hazard rate function, moments, Stress-strength parameter and order statistics of this distribution, this…
We formalize the intuitive idea of a labelled discrete surface which evolves in time, subject to two natural constraints: the evolution does not propagate information too fast; and it acts everywhere the same.
This article provides some characterizations of extended COM-Poisson distribution: conditional distribution given the sum, functional operator characterization (Stein identity). We also give some conditions such that the extended…
Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a…
We provide a new perspective on Stein's so-called density approach by introducing a new operator and characterizing class which are valid for a much wider family of probability distributions on the real line. We prove an elementary…
We strengthen a result of two of us on the existence of effective interactions for discretised continuous-spin models. We also point out that such an interaction cannot exist at very low temperatures. Moreover, we compare two ways of…
Phylogenetic inference aims to reconstruct the evolutionary relationships of different species based on genetic (or other) data. Discrete characters are a particular type of data, which contain information on how the species should be…
Computable Stein discrepancies have been deployed for a variety of applications, ranging from sampler selection in posterior inference to approximate Bayesian inference to goodness-of-fit testing. Existing convergence-determining Stein…
We propose a new general version of Stein's method for univariate distributions. In particular we propose a canonical definition of the Stein operator of a probability distribution {which is based on a linear difference or differential-type…
Over the last 80 years there has been much interest in the problem of finding an explicit formula for the probability density function of two zero mean correlated normal random variables. Motivated by this historical interest, we use a…
Stein discrepancies have emerged as a powerful statistical tool, being applied to fundamental statistical problems including parameter inference, goodness-of-fit testing, and sampling. The canonical Stein discrepancies require the…
In some fields of applications of stable distributions, especially in economics, it appears, that data have distributions similar to stable in a large region, but do not have such heavy tails. Our aim in this note is to propose several…
We provide a general result for finding Stein operators for the product of two independent random variables whose Stein operators satisfy a certain assumption, extending a recent result of Gaunt, Mijoule and Swan \cite{gms18}. This…
In the first part of the paper we use a new Fourier technique to obtain a Stein characterizations for random variables in the second Wiener chaos. We provide the connection between this result and similar conclusions that can be derived…
To what extent can we distinguish one probability distribution from another? Are there quantitative measures of distinguishability? The goal of this tutorial is to approach such questions by introducing the notion of the "distance" between…
This paper provides a fresh perspective on the representation of distributive bilattices and of related varieties. The techniques of naturalduality are employed to give, economically and in a uniform way, categories ofstructures dually…