相关论文: Moderate deviations for Poisson--Dirichlet distrib…

The Poisson distribution is the probability distribution of the number of independent events in a given period of time. Although the Poisson distribution appears ubiquitously in various stochastic dynamics of gene expression, both as…

We show that a slight modification of a theorem of Ruzmaikina and Aizenman on competing particle systems on the real line leads to a characterization of Poisson-Dirichlet distributions $PD(a,0)$. Precisely, let $s$ be a proper random…

Let $p_1 \ge p_2 \ge \dots$ be the prime factors of a random integer chosen uniformly from $1$ to $n$, and let $$ \frac{\log p_1}{\log n}, \frac{\log p_2}{\log n}, \dots $$ be the sequence of scaled log factors. Billingsley's Theorem…

In this paper we study finite velocity planar random motions with an infinite number of possible directions, where the number of changes of direction is randomized by means of an inhomogeneous fractional Poisson distribution. We first…

In this paper, we discuss the construction of a multivariate generalisation of the Dirichlet-multinomial distribution. An example from forensic genetics in the statistical analysis of DNA mixtures motivates the study of this multivariate…

In the stochastic network model of Britton and Lindholm [Dynamic random networks in dynamic populations. Journal of Statistical Physics, 2010], the number of individuals evolves according to a supercritical linear birth and death process,…

A novel over-dispersed discrete distribution, namely the PoiTG distribution is derived by the convolution of a Poisson variate and an independently distributed transmuted geometric random variable. This distribution generalizes the…

This paper presents a new derivation of the Generalized Poisson distribution. This distribution provides a good fit to the evolved, counts-in-cells distribution measured in numerical simulations of hierarchical clustering from Poisson…

This paper is devoted to a fractional generalization of the Dirichlet distribution. The form of the multivariate distribution is derived assuming that the $n$ partitions of the interval $[0,W_n]$ are independent and identically distributed…

In this article, we study a model of random permutations, which we call random standardized permutations, based on a sequence of i.i.d. random variables. This model generalizes others, such as the riffle-shuffle and the major-index-biased…

Moderate deviation principles for stochastic differential equations driven by a Poisson random measure (PRM) in finite and infinite dimensions are obtained. Proofs are based on a variational representation for expected values of positive…

Dirichlet process mixtures are flexible non-parametric models, particularly suited to density estimation and probabilistic clustering. In this work we study the posterior distribution induced by Dirichlet process mixtures as the sample size…

We consider a collection of fully coupled weakly interacting diffusion processes moving in a two-scale environment. We study the moderate deviations principle of the empirical distribution of the particles' positions in the combined limit…

This paper deals with U-statistics of Poisson processes and multiple Wiener-It\^o integrals on the Poisson space. Via sharp bounds on the cumulants for both classes of random variables, moderate deviation principles, concentration…

We use a functional analogue of the quantile function for probability measures on $\mathbb{R}^d$ to characterize a novel limit Poisson point process for radially recentred and rescaled random vectors under a radial-directional…

Consider an unlimited homogeneous medium disturbed by points generated via Poisson process. The neighborhood of a point plays an important role in spatial statistics problems. Here, we obtain analytically the distance statistics to $k$th…

We investigate the statistics of the mean magnetisation, of its large deviations and persistent large deviations in simple coarsening systems. We consider more specifically the case of the diffusion equation, of the Ising chain at zero…

Dirichlet distributions are commonly used for modeling vectors in a probability simplex. When used as a prior or a proposal distribution, it is natural to set the mean of a Dirichlet to be equal to the location where one wants the…

We study the distribution of large prime factors of a random element $u$ of arithmetic sequences satisfying simple regularity and equidistribution properties. We show that if such an arithmetic sequence has level of distribution $1$ the…

This note corrects a technical error in Guardiola (2020, Journal of Statistical Distributions and Applications), presents updated derivations, and offers an extended discussion of the properties of the spherical Dirichlet distribution.…