相关论文: Significance of the negative binomial distribution…

We analyze various data of multiplicity distributions by means of the Modified Negative Binomial Distribution (MNBD) and its KNO scaling function, since this MNBD explains the oscillating behavior of the cumulant moment observed in e^+e^-…

Multiplicity distributions $P(N)$ measured in multiparticle production processes are most frequently described by the Negative Binomial Distribution (NBD). However, with increasing collision energy some systematic discrepancies become more…

We develop a Bayesian nonparametric approach to a general family of latent class problems in which individuals can belong simultaneously to multiple classes and where each class can be exhibited multiple times by an individual. We introduce…

The sum of $n$ {non-independent} Bernoulli random variables could be modeled in several different ways. One of these is the Multiplicative Binomial Distribution (MBD), introduced by Altham (1978) and revised by Lovison (1998). In this work,…

Experiments at the Large Hadron Collider (LHC) have measured multiplicity distributions in proton-proton collisions at a new domain of center-of-mass energy ($\sqrt {s}$) in limited pseudorapidity intervals. We analyze multiplicity…

The seemingly disjoint problems of count and mixture modeling are united under the negative binomial (NB) process. A gamma process is employed to model the rate measure of a Poisson process, whose normalization provides a random probability…

By developing data augmentation methods unique to the negative binomial (NB) distribution, we unite seemingly disjoint count and mixture models under the NB process framework. We develop fundamental properties of the models and derive…

We discuss various statistical distributions of earthquake numbers. Previously we derived several discrete distributions to describe earthquake numbers for the branching model of earthquake occurrence: these distributions are the Poisson,…

A three-parameter discrete distribution is developed to describe the multiplicity distributions observed in total- and limited phase space volumes in different collision processes. The probability law is obtained by the Poisson transform of…

Recent theoretical developments revived the interest in charged particle multiplicities and their wide-spread parametrization, the negative binomial distribution (NBD). The central observable of the studies is the Shannon entropy of the…

Negative probabilities arise primarily in physics, statistical quantum mechanics and quantum computing. Negative probabilities arise as mixing distributions of unobserved latent variables in Bayesian modeling. Our goal is to provide a link…

Recent results in QCD on multiplicity distributions are briefly reviewed. QCD is able to predict very tiny features of multiplicity distributions which demonstrate that the negative binomial distribution (and, more generally, any infinitely…

The paper introduces the concept of a cluster structure to define a joint distribution of the sample size and its exchangeable random partitions. The cluster structure allows the probability distribution of the random partitions of a subset…

Using the Monte Carlo data at 7 TeV collected by the ATLAS collaboration (PYTHIA 6), we examine the necessity of applying the three-negative binomial distribution (T-NBD). By making use of the T-NBD formulation, we analyze the multiplicity…

This paper investigates the combinatorics that gives rise to the Boltzmann probability distribution. Despite being one of the most important distributions in physics and other fields of science, the mathematics of the underlying model of…

This study aims to analyze the data on multiplicity distributions and Bose-Einstein correlations collected at the LHC by the ATLAS and CMS Collaborations using a double-generalized Glauber-Lachs formula (D-GGL) and double-negative binomial…

A new multiplicity distribution with multifractal properties which can be used in high-energy physics and quantum optics is proposed. It may be considered as a generalization of the negative-binomial distribution. We find the structure of…

Classical statistics deals with determined and precise data analysis. But in reality, there are many cases where the information is not accurate and a degree of impreciseness, uncertainty, incompleteness, and vagueness is observed. In these…

The negative binomial distribution is self similar: If the spectrum over the whole rapidity range gives rise to a negative binomial, in absence of correlation and if the source is unique, also a partial range in rapidity gives rise to the…

The beta-negative binomial process (BNBP), an integer-valued stochastic process, is employed to partition a count vector into a latent random count matrix. As the marginal probability distribution of the BNBP that governs the exchangeable…