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Let X be a non-negative integer-valued random variable with probability function p(x) > 0 for every x in the support of X, S(x). For x0 ∈ S(x), let F(x0) = ∑x0 x=0 p(x) denote the distribution function of X at x0 and μ and σ 2 (0 < σ2 < ∞) denote the mean and variance of X, respectively. It is well known that the distribution of X can be approximated by some discrete distributions if their parameters are satisfied under certain conditions. Let Gp(x0) = ∑x0 x=0 pq x denote the geometric distribution function with parameter p = 1 − q at x0. If

AN IMPROVED BOUND ON GEOMETRIC APPROXIMATION BY w-FUNCTIONS