Related papers: Zero-Class Poisson for Rare-Event Studies
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…
In this paper, two parametric probability distributions capable to describe the statistics of X-ray photon detection by a CCD are presented. They are formulated from simple models that account for the pile-up phenomenon, in which two or…
Suppose we observe a Poisson process in real time for which the intensity may take on two possible values $\lambda_0$ and $\lambda_1$. Suppose further that the priori probability of the true intensity is not given. We solve a minimax…
Count data with zero inflation and large outliers are ubiquitous in many scientific applications. However, posterior analysis under a standard statistical model, such as Poisson or negative binomial distribution, is sensitive to such…
The analysis of count data is commonly done using Poisson models. Negative binomial models are a straightforward and readily motivated generalization for the case of overdispersed data, i.e., when the observed variance is greater than…
Count data with an excessive number of zeros frequently arise in fields such as economics, medicine, and public health. Traditional count models often fail to adequately handle such data, especially when the relationship between the…
Mixed Poisson distributions provide a flexible approach to the analysis of count data with overdispersion, zero inflation, or heavy tails. Since the Poisson mean must be nonnegative, the mixing distribution is typically assumed to have…
Object classes that surround us have a natural tendency to emerge at varying levels of abstraction. We propose a Bayesian approach to zero-shot learning (ZSL) that introduces the notion of meta-classes and implements a Bayesian hierarchy…
The paper addresses general aspects of experimental data analysis, dealing with the separation of ``signal vs. background''. It consists of two parts. Part I is a tutorial on statistical event classification, Bayesian inference, and test…
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…
In this paper, we propose a novel robust stochastic optimization approach with a distinctive consideration for rare events, in which divergence measures are used to bound the event-wise ambiguity sets. This is done by using the Poisson…
Current efforts to correctly categorize natural events from suspected explosion sources with data that is collected by ground- or space-based sensors presents historical challenges that remain unaddressed by the Event Categorization Matrix…
A frequent challenge encountered with compositional ecological data is how to interpret and model data with a high proportion of zeros and $N$'s. Such data frequently occur in ecological applications where counts of species are collected…
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…
The Zipf distribution is a probability distribution widely used by scientists from various disciplines due to its ubiquity. Some of these areas include linguistics, physics, genetics, and sociology, among others. In this paper, it is proved…
Bivariate count data arise in several different disciplines (epidemiology, marketing, sports statistics, etc., to name but a few) and the bivariate Poisson distribution which is a generalization of the Poisson distribution plays an…
An unbinned statistical test on cluster-like deviations from Poisson processes for point process data is introduced, presented in the context of time variability analysis of astrophysical sources in count rate experiments. The measure of…
In this paper, a new mixed Poisson distribution is introduced. This new distribution is obtained by utilizing mixing process, with Poisson distribution as mixed distribution and Transmuted Exponential distribution as mixing distribution.…
In this paper, we first use the distribution of the number of records to demonstrate that the right tail probabilities of counts of rare events are generally better approximated by the right tail probabilities of Poisson distribution than…
Statistical inference for extreme values of random events is difficult in practice due to low sample sizes and inaccurate models for the studied rare events. If prior knowledge for extreme values is available, Bayesian statistics can be…