Related papers: On the expected number of different records in a r…
We propose a new method for the calculation of the statistical properties, as e.g. the entropy, of unknown generators of symbolic sequences. The probability distribution $p(k)$ of the elements $k$ of a population can be approximated by the…
For an unknown continuous distribution on a real line, we consider the approximate estimation by the discretization. There are two methods for the discretization. First method is to divide the real line into several intervals before taking…
Given a sequence composed of a limit number of characters, we try to "read" it as a "text". This involves to segment the sequence into "words". The difficulty is to distinguish good segmentation from enormous number of random ones.Aiming at…
In this article we introduce associative Look-Up Tables. With their help, pseudo sums are correctly determined. The set of limit distributions in a pseudo-summation scheme of i.i.d. random variables is described. Also, two special cases…
In some socio-economic surveys, data are collected on sensitive or stigmatizing issues such as tax evasion, criminal conviction, drug use, etc. In such surveys, direct questioning of respondents is not of much use and the randomized…
We consider the problem of estimating the number of types in a corpus using the number of types observed in a sample of tokens from that corpus. We derive exact and asymptotic distributions for the number of observed types, conditioned upon…
The Gumbel trick is a method to sample from a discrete probability distribution, or to estimate its normalizing partition function. The method relies on repeatedly applying a random perturbation to the distribution in a particular way, each…
We consider a multinomial distribution, where the number of cells increases and the cell-probabilities decreases as the number of observations grows. The probabilities of large deviations of statistics, which has form of a sum of Borel…
This paper studies the problem of finding the median of N distinct numbers distributed across networked agents. Each agent updates its estimate for the median from noisy local observations of one of the N numbers and information from…
Given a correlation generated by a (possibly quantum) communication network, we study the amount of shared randomness required to generate it. We develop a novel upper bound for approximating distributions generated by arbitrary networks…
Motivated by the need, in some Bayesian likelihood free inference problems, of imputing a multivariate counting distribution based on its vector of means and variance-covariance matrix, we define a generic multivariate discrete…
We initiate a systematic investigation of distribution testing in the framework of algorithmic replicability. Specifically, given independent samples from a collection of probability distributions, the goal is to characterize the sample…
An equivalent condition for the product of elements of an independent random sample on a compact algebraic group converging in distribution to some random variable as the sample size increases is obtained. Namely, a limit distribution…
In this paper we introduce randomized $t$-type statistics that will be referred to as randomized pivots. We show that these randomized pivots yield central limit theorems with a significantly smaller magnitude of error as compared to that…
The purpose of this paper is to study the problem of estimating a compactly supported density of probability from noisy observations of its moments. In fact, we provide a statistical approach to the famous Hausdorff classical moment…
Sampling distribution, a foundational concept in statistics, is difficult to understand, since we usually have only one realization of the estimator of interest. In this work, we present an innovative method for helping university students…
We study the fundamental problem of estimating an unknown discrete distribution $p$ over $d$ symbols, given $n$ i.i.d. samples from the distribution. We are interested in minimizing the KL divergence between the true distribution and the…
We study distribution testing in the standard access model and the conditional access model when the memory available to the testing algorithm is bounded. In both scenarios, the samples appear in an online fashion and the goal is to test…
We consider the problem of estimating the joint distribution of $n$ independent random variables. Our approach is based on a family of candidate probabilities that we shall call a model and which is chosen to either contain the true…
Zipf's law is a hallmark of several complex systems with a modular structure, such as books composed by words or genomes composed by genes. In these component systems, Zipf's law describes the empirical power law distribution of component…