The limit theorem for dependent Beernoulli tests

Abstract

© Published under licence by IOP Publishing Ltd. There is considered the generalized Bernoulli tests scheme in which it is assumed that the tests are connected unlike the usual Bernoulli tests scheme. There is defined the condition of weak dependence of tests. The integral limit theorem is proved for the distribution of the number of successes in carrying out a finite set of tests. There is investigated the convergence rate in the limit theorem. There is obtained the optimal remainder.