On a generalization of the binomial distribution and its Poisson-like limit

TL;DR

This paper introduces a generalized binomial distribution linked to a sequence of numbers, proves its Poisson-like limit, and discusses conditions for its probabilistic interpretation, with potential applications in quantum optics.

Contribution

It presents a new generalization of the binomial distribution, establishes its Poisson-like limit, and analyzes conditions for probabilistic interpretation, expanding understanding in quantum optics contexts.

Findings

Established a Poisson-like limit for the generalized distribution

Identified conditions for probabilistic interpretation

Potential applications in quantum optics with imperfect detection

Abstract

We examine a generalization of the binomial distribution associated with a strictly increasing sequence of numbers and we prove its Poisson-like limit. Such generalizations might be found in quantum optics with imperfect detection. We discuss under which conditions this distribution can have a probabilistic interpretation.