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On composed Poisson distributions, IV

Remarks on the theory of differential processes

Acta Mathematica Hungarica
András Prékopa
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Let A 1,...,A N and B 1,...,B M be two sequences of events and let ν N(A) and ν M(B) be the number of those A i and B j, respectively, that occur. Based on multivariate Lagrange interpolation, we give a method that yields linear bounds in terms of S k,t, k+tm on the distribution of the vector (ν N(A), ν M(B)). For the same value of m, several inequalities can be generated and all of them are best bounds for some values of S k,t. Known bivariate Bonferroni-type inequalities are reconstructed and new inequalities are generated, too.

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