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arXiv · 2202.09838

Extensions of two classical Poisson limit laws to non-stationary independent data

Aladji Babacar Niang·Harouna Sangaré·Tchilabalo Abozou Kpanzou·Gane Samb Lo·Nafy Ngom
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Abstract

In earlier stages in the introduction to asymptotic methods in probability theory, the weak convergence of sequences $(X_n)_{n\geq 1}$ of Binomial of random variables (\textit{rv}'s) to a Poisson law is classical and easy-to prove. A version of such a result concerning sequences $(Y_n)_{n\geq 1}$ of negative binomial \textit{rv}'s also exists. In both cases, $X_n$ and $Y_n-n$ are by-row sums $S_n[X]$ and $S_n[Y]$ of arrays of Bernoulli \textit{rv}'s and corrected geometric \textit{rv}'s respectively. When considered in the general frame of asymptotic theorems of by-row sums of \textit{rv}'s of arrays, these two simple results in the independent and identically distributed scheme can be generalized to non-stationary data and beyond to non-stationary and dependent data. Further generalizations give interesting results that would not be found by direct methods. In this paper, we focus on generalizations to the non-stationary independent data. Extensions to dependent data will addressed later.

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Aladji Babacar Niang, Harouna Sangaré, Tchilabalo Abozou Kpanzou, Gane Samb Lo, Nafy Ngom. 2022-02-20. Extensions of two classical Poisson limit laws to non-stationary independent data. https://arxiv.org/abs/2202.09838

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