Some results on r-truncated degenerate Poisson Random Variables

TL;DR

This paper introduces the r-truncated degenerate Poisson distribution, exploring its properties and extending the understanding of truncated Poisson models in probability theory.

Contribution

It presents the first study of r-truncated degenerate Poisson random variables and analyzes their fundamental properties.

Findings

Defined the r-truncated degenerate Poisson distribution

Derived key properties and formulas for the distribution

Extended the theory of truncated Poisson models

Abstract

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 this paper, we introduce the r-truncated degenerate Poisson random variable with parameter a and investigate various properties of this random variable