Poisson approximation to the binomial distribution: extensions to the convergence of positive operators Article Swipe

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Poisson distribution Mathematics Mathematical proof Convergence (economics) Applied mathematics Limit (mathematics) Binomial (polynomial) Negative binomial distribution Binomial distribution Probabilistic logic Poisson binomial distribution Binomial approximation Distribution (mathematics) Discrete mathematics Statistics Mathematical analysis Economic growth Geometry Economics Beta-binomial distribution

Ana Maria Acu , Margareta Heilmann , Ioan Raşa , Andra Seserman ·

YOU? · · 2022 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2208.08326 · OA: W4300406472

The idea behind Poisson approximation to the binomial distribution was used in [J. de la Cal, F. Luquin, J. Approx. Theory, 68(3), 1992, 322-329] and subsequent papers in order to establish the convergence of suitable sequences of positive linear operators. The proofs in these papers are given using probabilistic methods. We use similar methods, but in analytic terms. In this way we recover some known results and establish several new ones. In particular, we enlarge the list of the limit operators and give characterizations of them.