Poisson approximations for sequences of random variables
It is well known in the general theory of the central limit problem that sums of independent random variables can always be approximated by sums of Poisson type of variables without effecting asymptotic properties. However, Poisson type of random variables is no longer defined on the nonnegative integers. The author proposes an approximation by a Poisson distribution to sums of independent and identically distributed lattice variables after proper centering. Speed of convergence is discussed and compared with the speed of normal approximation. For the underlying variables, the \((2+a)\)-th moment is assumed to be finite, \(a>0\).
scientific article; zbMATH DE number 1202781
scientific article