In this paper we derive the central limit theorem for $\sum\nolimits_{i = 1}^n {{a_{ni}}{\xi _i}} $, where {ani, 1 ≤ i ≤ n} is a triangular array of nonnegative numbers such that supn ...

The usual local central limit theorem provides an approximation for the probability for an iid sequence . The approximation is proportional to the lattice size of the underlying distribution of the ...