Related papers: Characterizations of non-normalized discrete proba…
Stein's (1972) method is a very general tool for assessing the quality of approximation of the distribution of a random element by another, often simpler, distribution. In applications of Stein's method, one needs to establish a Stein…
This paper is a short exposition of Stein's method of normal approximation from my personal perspective. It focuses mainly on the characterization of the normal distribution and the construction of Stein identities. Through examples, it…
Stein's method provides a way of bounding the distance of a probability distribution to a target distribution $\mu$. Here we develop Stein's method for the class of discrete Gibbs measures with a density $e^V$, where $V$ is the energy…
We describe a statistical method to avoid biased estimation of the content of different particle species. We consider the case when the particle identification information strongly depends on some kinematical variables, whose distributions…
We approximate the distribution of the sum of independent but not necessarily identically distributed Bernoulli random variables using a shifted binomial distribution where the three parameters (the number of trials, the probability of…
We explore the asymptotic distributions of sequences of integer-valued additive functions defined on the symmetric group endowed with the Ewens probability measure as the order of the group increases. Applying the method of factorial…
As an application of Stein's method for Poisson approximation, we prove rates of convergence for the tail probabilities of two scan statistics that have been suggested for detecting local signals in sequences of independent random variables…
A tempered version of the discrete Linnik distribution is introduced in order to obtain integer-valued distribution families connected to stable laws. The proposal constitutes a generalization of the well-known Poisson-Tweedie law, which is…
Stable distributions are of fundamental importance in probability theory, yet their absolute continuity makes them unsuitable for modeling count data. A discrete analog of strict stability has been previously proposed by replacing scaling…
A Poisson Binomial distribution over $n$ variables is the distribution of the sum of $n$ independent Bernoullis. We provide a sample near-optimal algorithm for testing whether a distribution $P$ supported on $\{0,...,n\}$ to which we have…
In this paper we develop a very general class of bivariate discrete distributions. The basic idea is very simple. The marginals are obtained by taking the random geometric sum of a baseline distribution function. The proposed class of…
Stein's method is used to approximate sums of discrete and locally dependent random variables by a centered and symmetric Binomial distribution. Under appropriate smoothness properties of the summands, the same order of accuracy as in the…
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…
Contrary to standard statistical models, unnormalised statistical models only specify the likelihood function up to a constant. While such models are natural and popular, the lack of normalisation makes inference much more difficult. Here…
In this article, we obtain, for the total variance distance, the error bounds between Poisson and convolution of power series distributions via Stein's method. This provides a unified approach to many known discrete distributions. Several…
An important functional of Poisson random measure is the negative binomial process (NBP). We use NBP to introduce a generalized Poisson-Kingman distribution and its corresponding random discrete probability measure. This random discrete…
Following the student t-statistic, normalization has been a widely used method in statistic and other disciplines including economics, ecology and machine learning. We focus on statistics taking the form of a ratio over (some power of) the…
There is given a characterization of the geometric distribution by the independence of linear forms with random coefficients. The result is a discrete analog of the corresponding theorem on exponential distribution. The property of linear…
We introduce a version of Stein's method of comparison of operators specifically tailored to the problem of bounding the Wasserstein-1 distance between continuous and discrete distributions on the real line. Our approach rests on a new…
In [Schuhmacher, Electron. J. Probab. 10 (2005), 165--201] estimates of the Barbour-Brown distance d_2 between the distribution of a thinned point process and the distribution of a Poisson process were derived by combining discretization…