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On the Poisson approximation of random diagonal sums of Bernoulli matrices

Roos Bero

Probability and Mathematical Statistics

2024

Vol. 44, Fasc. 2

237--265

We use the Stein-Chen method to prove new explicit inequalities for the total variation, Wasserstein and local distances between the distribution of a random diagonal sum of a Bernoulli matrix and a Poisson distribution. Approximation results using a finite signed measure of higher order are given as well. Some of our total variation bounds improve existing results in the literature.