相关论文: On the accuracy of the poissonisation in the infin…

The paper concerns the classical occupancy scheme with infinitely many boxes. We establish approximations to the distributions of the number of occupied boxes, and of the number of boxes containing exactly r balls, within the family of…

This article studies the expected occupancy probabilities on an alphabet. Unlike the standard situation, where observations are assumed to be independent and identically distributed (iid), we assume that they follow a regime switching…

This paper collects facts about the number of occupied boxes in the classical balls-in-boxes occupancy scheme with infinitely many positive frequencies: equivalently, about the number of species represented in samples from populations with…

In this paper, we study an asymptotic approximation of the Fisher information for the estimation of a scalar parameter using quantized measurements. We show that, as the number of quantization intervals tends to infinity, the loss of Fisher…

In the classical occupancy scheme, one considers a fixed discrete probability measure ${\bf p}=(p_i: {i\in{\cal I}})$ and throws balls independently at random in boxes labeled by ${\cal I}$, such that $p_i$ is the probability that a given…

Optimal values and solutions of empirical approximations of stochastic optimization problems can be viewed as statistical estimators of their true values. From this perspective, it is important to understand the asymptotic behavior of these…

An infinite urn scheme is defined by a probability mass function $(p_j)_{j\geq1}$ over positive integers. A random allocation consists of a sample of $N$ independent drawings according to this probability distribution where $N$ may be…

We use the martingale-theoretic approach of game-theoretic probability to incorporate imprecision into the study of randomness. In particular, we define a notion of computable randomness associated with interval, rather than precise,…

For a probability distribution $P$ on an at most countable alphabet $\mathcal A$, this article gives finite sample bounds for the expected occupancy counts $\mathbb E K_{n,r}$ and probabilities $\mathbb E M_{n,r}$. Both upper and lower…

We use the martingale-theoretic approach of game-theoretic probability to incorporate imprecision into the study of randomness. In particular, we define several notions of randomness associated with interval, rather than precise,…

We construct a new sufficient conditions for boundedness or continuity of arbitrary random fields relying on the so-called partition scheme, alike in the classical majorizing measure method. We deduce also the used in the practice…

Consider $ m $ copies of an irreducible, aperiodic Markov chain $ Y $ taking values in a finite state space. The asymptotics as $ m $ tends to infinity, of the first time from which on the trajectories of the $ m $ copies differ, have been…

In this paper we continue our earlier investigations into the asymptotic behaviour of infinite systems of coupled differential equations. Under the mild assumption that the so-called characteristic function of our system is completely…

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 revisit a version of the classic occupancy scheme, where balls are thrown until almost all boxes receive a given number of balls. Special cases are widely known as coupon-collectors and dixie cup problems. We show that as the number of…

Here we present an analytic approximation for the entropy of floating-point numbers, along with bounds on the error of this approximation. It is well-known that the differential entropy is tightly linked to the discrete entropy of a…

We review approaches to statistical inference based on randomization. Permutation tests are treated as an important special case. Under a certain group invariance property, referred to as the ``randomization hypothesis,'' randomization…

The Bernoulli sieve is an infinite occupancy scheme obtained by allocating the points of a uniform $[0,1]$ sample over an infinite collection of intervals made up by successive positions of a multiplicative random walk independent of the…

Convergence rate estimates in limit theorems for sums of independent random variables are considered.

We consider an infinite balls-in-boxes occupancy scheme with boxes organised in nested hierarchy, and random probabilities of boxes defined in terms of iterated fragmentation of a unit mass. We obtain a multivariate functional limit theorem…