In this paper we propose an approximate method to estimate the cell loss probability(CLP) due to buffer overflow in ATM networks. The main idea is to relate the buffer capacity with the CLP target in explicit formula by using the approximate upper bound for the tail distribution of a queue. The significance of the proposition lies in the fact that we can obtain the expected CLP by using only the source traffic data represented by mean rate and its variance. To that purpose we consider the problem of estimating the cell loss measures form the statistical viewpoint such that the probability of cell loss due to buffer overflow does not exceed a target value. In obtaining the exact solution we use a typical matrix analytic method for GI/D/1B queue where B is the queue size. Finally, in order to investigate the accuracy of the result, we present both the approximate and exact results of the numerical computation and give some discussion.