Related papers: Poisson and Compound Poisson Approximations in a N…
This paper introduces constrained mixtures for continuous distributions, characterized by a mixture of distributions where each distribution has a shape similar to the base distribution and disjoint domains. This new concept is used to…
In this paper, we introduce a new approach to generate flexible parametric families of distributions. These models arise on competitive and complementary risks scenario, in which the lifetime associated with a particular risk is not…
Mixed Poisson distributions provide a flexible approach to the analysis of count data with overdispersion, zero inflation, or heavy tails. Since the Poisson mean must be nonnegative, the mixing distribution is typically assumed to have…
Tempered distributions on Rn that have the Poisson structure are characterized in terms of geometry of its support and spectrum
A compound Poisson process whose parameters are all unknown is observed at finitely many equispaced times. Nonparametric estimators of the jump and L\'evy distributions are proposed and functional central limit theorems using the uniform…
This is my dissertation. Its research object is a symmetric group of permutations acting on a finite set. The density of permutations with a given cycle structure pattern is explored when the group order tends to infinity. New and sharper…
This paper establishes expectation and variance asymptotics for statistics of the Poisson--Voronoi approximation of general sets, as the underlying intensity of the Poisson point process tends to infinity. Statistics of interest include…
We prove the asymptotic functional Poisson laws in the total variation norm and obtain estimates of the corresponding convergence rates for a large class of hyperbolic dynamical systems. These results generalize the ones obtained before in…
In this paper, we study compound bi-free Poisson distributions for {\sl two-faced families of random variables}. We prove a Poisson limit theorem for compound bi-free Poisson distributions. Furthermore, a bi-free infinitely divisible…
We give a general framework for approximations to combinatorial assemblies, especially suitable to the situation where the number $k$ of components is specified, in addition to the overall size $n$. This involves a Poisson process, which,…
Based on the probability generating function of stuttering Poisson distribution (SPD), this paper considers some equivalent propositions of SPD. From this, we show that some distributions in the application of non-life insurance actuarial…
We construct an asymptotic approximation to the solution of a transmission problem for a body containing a region occupied by many small inclusions. The cluster of inclusions is characterised by two small parameters that determine the…
In this paper, we propose a discrete circular distribution obtained by extending the wrapped Poisson distribution. This new distribution, the Invariant Wrapped Poisson (IWP), enjoys numerous advantages: simple tractable density,…
We develop a diffusion approximation for systems subject to fast random resetting by small amplitudes. Equivalently, this describes systems with frequent but small catastrophes. We demonstrate the validity of the approximation by computing…
With any symmetric distribution $\mu$ on the real line we may associate a parametric family of noncentral distributions as the distributions of $(X+\delta)^2$, $\delta\not=0$, where $X$ is a random variable with distribution $\mu$. The…
The Poisson distribution arises naturally when dealing with data involving counts, and it has found many applications in inverse problems and imaging. In this work, we develop an approximate Bayesian inference technique based on expectation…
By a mixture density is meant a density of the form $\pi_{\mu}(\cdot)=\int\pi_{\theta}(\cdot)\times\mu(d\theta)$, where $(\pi_{\theta})_{\theta\in\Theta}$ is a family of probability densities and $\mu$ is a probability measure on $\Theta$.…
We determine the joint limiting distribution of adjacent spacings around a central, intermediate, or an extreme order statistic $X_{k:n}$ of a random sample of size $n$ from a continuous distribution $F$. For central and intermediate cases,…
Given a set of independent Poisson random variables with common mean, we study the distribution of their maximum and obtain an accurate asymptotic formula to locate the most probable value of the maximum. We verify our analytic results with…
We exploit a suitable moment-based characterization of the mixture of Poisson distribution for developing Bayesian inference for the unknown size of a finite population whose units are subject to multiple occurrences during an enumeration…