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Большой семинар кафедры теории вероятностей МГУ
6 марта 2024 г. 16:45, г. Москва, ГЗ МГУ, ауд. 12-24
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[Three-parameter distributional approximations for sums of locally dependent random variables]
Zhonggen Su
School of Mathematical Sciences, Zhejiang University
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Аннотация:
Consider a finite family of locally dependent non-negative integer-valued random variables with finite third order moments, and denote by W their sum. There have been a number of research works on computing the distributions of W in literature. In this talk I shall report a recent work on three-Parameter distributional approximation for W. Specifically speaking, denote by M a three parameter random variable, say the mixture of Bernoulli binomial distribution and Poisson distribution, the mixture of negative binomial distribution and Poisson distribution or the mixture of Poisson distributions. We use Stein's method to establish general upper error bounds for the total variation distance between W and M, where three parameters in M are uniquely determined by the first three moments of W. As a direct consequence, we obtain a discretized normal approximation for W. To illustrate, we study in detail a few of well-known examples, among which are counting vertices of all edges point inward, birthday problem, counting monochromatic edges in uniformly colored graphs, and triangles in the Erdős–Rényi random graph. Through delicate analysis and computations, we obtain sharper upper error bounds than existing results. This talk is based on recent joint works with Xiaolin Wang.
Язык доклада: английский
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