A new method for obtaining sharp compound Poisson approximation error estimates for sums of locally dependent random variables
The authors develop probabilistic techniques (the employment of ideal probability metrics, stochastic orders and the coupling method) to establish sharp bounds for the total variation distance between the distribution of the sum of integer-valued independent or \(k\)-dependent random variables and appropriate Poisson or compound Poisson law. These bounds contain the smoothness factor, i.e., the \(L_1\)-norm of the second-order difference of the probability distribution function of the approximating law. The obtained results are compared with well-known ones proven by the Stein-Chen method. Some examples concerning the appearances of rare runs in a sequence of Bernoulli trials are provided to illustrate the effectiveness of the paper's main results.
sums of independent integer-valued random variables
scientific article; zbMATH DE number 6083965
scientific article