Generalized Poisson Distributions as Limits of Sums for Arrays of Dependent Random Vectors

Arrays of random vectors with values in Rd stationary in rows, are investigated. By the assumptions related to the ones used in the extreme value theory a limit thoerem for sums is proved. Necessary and sufficient conditions for the convergence in distribution of sums to some generalized Poisson distributions in m-dependent and [alpha]-, [rho]-, [phi]-mixing cases are given. As a tool the point processes theory is used.