Random central limit theorem for associated random variables and the order of approximation

We consider a random number Nn and strictly stationary associated random variables Xk and form random partial sums SNn=∑j=1NnXj under the assumption that Nn is independent of the sequence {Xr,r≥1} for every n≥1. Under certain conditions on the random variables Xk and Nn, we obtain the limit distribution of the sequence SNn after suitable normalization. We also obtain an estimate of the order of approximation.