Related papers: Poisson approximation
Given a statistical model, we propose a novel estimation method that yields randomised estimators for the unknown distribution of an observed random variable. We establish non-asymptotic bounds for the performance of these estimators and…
In the era of open data, Poisson and other count regression models are increasingly important. Still, conventional Poisson regression has remaining issues in terms of identifiability and computational efficiency. Especially, due to an…
We consider a finite sequence of random points in a finite domain of a finite-dimensional Euclidean space. The points are sequentially allocated in the domain according to a model of cooperative sequential adsorption. The main peculiarity…
The classical Poisson theorem says that if $\xi_1,\xi_2,...$ are i.i.d. 0--1 Bernoulli random variables taking on 1 with probability $p_n\equiv \la/n$ then the sum $S_n=\sum_{i=1}^n\xi_i$ is asymptotically in $n$ Poisson distributed with…
The subset sum problem is known to be an NP-hard problem in the field of computer science with the fastest known approach having a run-time complexity of $O(2^{0.3113n})$. A modified version of this problem is known as the perfect sum…
Motivated by the Central Limit Theorem, in this paper, we study both universal and non-universal simulations of random variables with an arbitrary target distribution $Q_{Y}$ by general mappings, not limited to linear ones (as in the…
Approximation theory is concerned with the ability to approximate functions by simpler and more easily calculated functions. The first question we ask in approximation theory concerns the {\it possibility of approximation}. Is the given…
The Gaussian theory of errors has been generalized to situations, where the Gaussian distribution and, hence, the Gaussian rules of error propagation are inadequate. The generalizations are based on Bayes' theorem and a suitable measure.…
The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the…
We use Stein's method to obtain bounds on the rate of convergence for a class of statistics in geometric probability obtained as a sum of contributions from Poisson points which are exponentially stabilizing, i.e. locally determined in a…
We consider distributional approximation by generalized Dickman distributions, which appear in number theory, perpetuities, logarithmic combinatorial structures and many other areas. We prove bounds in the Kolmogorov distance for the…
The possibility of construction of continuous analogue of Poisson distribution with the search of bounds of confidence intervals for parameter of Poisson distribution is discussed. Also, in the article is shown that the true value of a…
We give a survey on the concept of Poissonian pair correlation (PPC) of sequences in the unit interval, on existing and recent results and we state a list of open problems. Moreover, we present and discuss a quite recent multi-dimensional…
Asymptotic behavior of the point process of high and medium values of a Gaussian stationary process with discrete time is considered. An approximation by a Poisson cluster point process is given for the point process.
This paper is an overview of the classical level crossing problem which is studied extensively in the literature and is fundamental in many branches of applied probability. We discuss a number of approximations with an emphasis on their…
We consider the discrete three dimensional scan statistics. Viewed as the maximum of an 1-dependent stationary r.v.'s sequence, we provide approximations and error bounds for the probability distribution of the three dimensional scan…
Let $S_n=I_1+\cdots+I_n$ be a sum of independent indicators $I_i$, with $p_i=\Pr(I_i=1)=1-\Pr(I_i=0)$, $i=1,\ldots,n$. It is well-known that the total variation distance between $S_n$ and $Z_\lambda$, where $Z_\lambda$ has a Poisson…
In this paper, we develop a general theory on the coverage probability of random intervals defined in terms of discrete random variables with continuous parameter spaces. The theory shows that the minimum coverage probabilities of random…
We show that for all $\psi$-mixing shifts distributions of the numbers of multiple recurrencies to shrinking cylindrical neighborhoods of all points are close either to Poisson or to compound Poisson distributions. We also describe…
This paper gives a review of concentration inequalities which are widely employed in non-asymptotical analyses of mathematical statistics in a wide range of settings, from distribution-free to distribution-dependent, from sub-Gaussian to…