Related papers: Exploring the Zipf Distribution Through the Lens o…
We investigate the distribution of the volume and coordination number associated to each particle in a jammed packing of monodisperse hard sphere using the mesoscopic ensemble developed in Nature 453, 606 (2008). Theory predicts an…
Textual geographic information is indispensable and heavily relied upon in practical applications. The absence of clear distribution poses challenges in effectively harnessing geographic information, thereby driving our quest for…
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…
Zipf's law is just one out of many universal laws proposed to describe statistical regularities in language. Here we review and critically discuss how these laws can be statistically interpreted, fitted, and tested (falsified). The modern…
We overview results on the topic of Poisson approximation that are missed in existing surveys. The topic of Poisson approximation to the distribution of a sum of integer-valued random variables is presented as well. We do not restrict…
The repeated presentation of an identical visual stimulus in the receptive field of a neuron may evoke different spiking patterns at each trial. Probabilistic methods are essential to understand the functional role of this variance within…
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…
This work considers a problem of estimating a mixing probability density $f$ in the setting of discrete mixture models. The paper consists of three parts. The first part focuses on the construction of an $L_1$ consistent estimator of $f$.…
Mutual information is one of the essential building blocks of information theory. Yet, it is only finitely defined for distributions with fast decaying tails on a countable joint alphabet of two random elements. The unboundedness of mutual…
The mollified uniform distribution is rediscovered, which constitutes a ``soft'' version of the continuous uniform distribution. Important stochastic properties are presented and used to demonstrate potential fields of applications. For…
In this paper, a statistical analysis of the structure of one blog community, a kind of social networks, is presented. The quantities such as degree distribution, clustering coefficient, average shortest path length are calculated to…
In this paper we deal with the structural properties of weighted networks. Starting from an empirical analysis of a linguistic network, we analyse the differences between the statistical properties of a real and a shuffled network and we…
This book is devoted to the problem of sequential probability forecasting, that is, predicting the probabilities of the next outcome of a growing sequence of observations given the past. This problem is considered in a very general setting…
This paper examines the classical matching distribution arising in the "problem of coincidences". We generalise the classical matching distribution with a preliminary round of allocation where items are correctly matched with some fixed…
A systematic study of the probability distribution of superimposed random codes is presented through the use of generating functions. Special attention is paid to the cases of either uniformly distributed but not necessarily independent or…
Zipf's law is the main regularity of quantitative linguistics. Despite of many works devoted to foundations of this law, it is still unclear whether it is only a statistical regularity, or it has deeper relations with information-carrying…
This article brings in two new discrete distributions: multidimensional Binomial distribution and multidimensional Poisson distribution. Those distributions were created in eventology as more correct generalizations of Binomial and Poisson…
The double Dixie cup problem of D.J. Newman and L. Shepp is a well-known variant of the coupon collector problem, where the object of study is the number of coupons that a collector has to buy in order to complete m sets of all N existing…
If f is a polynomial with integer coefficients and q is an integer, we may regard f as a map from Z/qZ to Z/qZ. We show that the distribution of the (normalized) spacings between consecutive elements in the image of these maps becomes…
Unifying the generalized Marshall-Olkin (GMO) and Poisson-G (P-G) a new family of distribution is proposed. Density and the survival function are expressed as infinite mixtures of P-G family. The quantile function, asymptotes, shapes,…