On the Count Probability of Many Correlated Symmetric Events

2019/10/29 by Rüdiger Kürsten, Kürsten, Rüdiger
Computer Science · Decision Sciences · Mathematics · #60C05 #60E10 #Bayesian Modeling and Causal Inference #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1910.13468

openalex publication_date 2019/10/29 · openalex created_date 2019/11/08 · openalex updated_date 2026/07/28

Abstract

We consider N events that are defined on a common probability space. Those events shell have a common probability function that is symmetric with respect to interchanging the events. We ask for the probability distribution of the number of events that occur. If the probability of a single event is proportional to 1/N the resulting count probability is Poisson distributed in the limit of N→ ∞ for independent events. In this paper we calculate the characteristic function of the limiting count probability distribution for events that are correlated up to an arbitrary but finite order.

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