Resumen de A note on Poisson approximation

Paul Deheuvels

• español

  En este trabajo consideramos evaluaciones de la distancia en variación entre leyes de Poisson, binomial y de sumas variables de Bernoulli independientes.

• English

  We obtain in this note evaluations of the total variation distance and of the Kolmogorov-Smirnov distance between the sum of n random variables with non identical Bernoulli distributions and a Poisson distribution. Some of our results precise bounds obtained by Le Cam, Serfling, Barbour and Hall.

  It is shown, among other results, that if p1 = P (X1=1), ..., pn = P (Xn=1) satisfy some appropriate conditions, such that p = 1/n Sipi ? 0, np ? 8, np2 ? 0, then the total variation distance between X1+...+Xn and a Poisson distribution with expectation np is p(2?e)-1/2(1 + o(1)).