Abstract
Let X-1, X-2,..,X-N be independent, identically distributed, non-negative, integervalued random variables and let N be a non-negative, integer-valued random variable independent of X-1, X-2,..,X-N. In this paper, we consider two nonparametric estimation problems for the random sum variable S-N = Sigma(N)(i=1) X-i, S-0= X-0= 0. The first is the estimation of the means of X-i and N based on the second-moment assumptions on distributions of X-i and N. The second is the nonparametric estimation of the distribution of X-i given a parametric model for the distribution of N. Some asymptotic properties of the proposed estimators are discussed.