Poisson approximations of multinomial distributions and point processes
The authors extend their operator treatment of Poisson approximations of sums of independent Bernoulli random variables [Ann. Probab. 14, 663-676 (1986; Zbl 0597.60019)] to the setting of multivariate Bernoulli summands. If the summands are identically distributed, the distance estimates follow from the univariate case [by an observation of Michel, ASTIN Bull. (1987)]. In general, a leading term estimate for the total variation distance is obtained, together with an error estimate which, however, is not yet ideal in the case equivalent, in the univariate setting, to \(\sum_{i}p^ 2_ i\to \infty\).
operator treatment of Poisson approximations
scientific article; zbMATH DE number 4062283
scientific article