Related papers: Exploring the Zipf Distribution Through the Lens o…
The zero-truncated Poisson distributions are certain discrete probability distributions whose supports are the set of positive integers, which are also known as the conditional Poisson distributions or the positive Poisson distributions. In…
The negative binomial distribution has been widely used as a more flexible model than the Poisson distribution for count data. However, when the true data-generating process is Poisson, it is often challenging to distinguish it from a…
The paper presents a new statistical method that enables the use of systematic errors in the maximum-likelihood regression of integer-count Poisson data to a parametric model. The method is primarily aimed at the characterization of the…
Zipf's law is a fundamental paradigm in the statistics of written and spoken natural language as well as in other communication systems. We raise the question of the elementary units for which Zipf's law should hold in the most natural way,…
Zero-inflated count data arise in various fields, including health, biology, economics, and the social sciences. These data are often modelled using probabilistic distributions such as zero-inflated Poisson (ZIP), zero-inflated negative…
I examine the phenomenology of particle multiplicity distributions, with special emphasis on the low multiplicities that are a background in the study of rapidity gaps. In particular, I analyze the multiplicity distribution in a rapidity…
Bimodal truncated count distributions are frequently observed in aggregate survey data and in user ratings when respondents are mixed in their opinion. They also arise in censored count data, where the highest category might create an…
We present new mixture representations for the generalized Linnik distribution in terms of normal, Laplace, exponential and stable laws and establish the relationship between the mixing distributions in these representations. Based on these…
In this work, we study the partial sums of independent and identically distributed random variables with the number of terms following a fractional Poisson (FP) distribution. The FP sum contains the Poisson and geometric summations as…
We present an overview of possible reasons for the appearance of heavy-tailed distributions in applications to the natural sciences. These distributions include the laws of Pareto, Lotka, and some new ones. The reasons are illustrated using…
The rank-size plots of a large number of different physical and socio-economic systems are usually said to follow Zipf's law, but a unique framework for the comprehension of this ubiquitous scaling law is still lacking. Here we show that a…
For testing goodness of fit it is very popular to use either the chi square statistic or G statistics (information divergence). Asymptotically both are chi square distributed so an obvious question is which of the two statistics that has a…
The frequency of the preferred order for a noun phrase formed by demonstrative, numeral, adjective and noun has received significant attention over the last two decades. We investigate the actual distribution of the 24 possible orders.…
Matrix-form Poisson probability distributions were recently introduced as one matrix generalization of Panjer distributions. We show in this paper that under the constraint that their representation is to be nonnegative, they have a…
A family of consistent tests, derived from a characterization of the probability generating function, is proposed for assessing Poissonity against a wide class of count distributions, which includes some of the most frequently adopted…
Scientific cooperation on an international level has been well studied in the literature. However, much less is known about this cooperation on the intercontinental level. In this paper, we address this issue by creating a collection of…
Power-law distributions with various exponents are studied. We first introduce a simple and generic model that reproduces Zipf's law. We can regard this model both as the time evolution of the population of cities and that of the asset…
We address the role of multiplicative stochastic processes in modeling the occurrence of power-law city size distributions. As an explanation of the result of Zipf's rank analysis, Simon's model is presented in a mathematically elementary…
Zipf's power law is a general empirical regularity found in many natural and social systems. A recently developed theory predicts that Zipf's law corresponds to systems that are growing according to a maximally sustainable path in the…
It turns out that some empirical facts in Big Data are the effects of properties of large numbers. Zipf's law 'noise' is an example of such an artefact. We expose several properties of the power law distributions and of similar distribution…