A Compound Poisson Convergence Theorem for Sums of m-Dependent Variables
نویسنده
چکیده
We prove the Simons-Johnson theorem for the sums Sn of m-dependent random variables, with exponential weights and limiting compound Poisson distribution CP(s, λ). More precisely, we give sufficient conditions for ∑ ∞ k=0 ehk|P (Sn = k)−CP(s, λ){k}| → 0 and provide an estimate on the rate of convergence. It is shown that the Simons-Johnson theorem holds for weighted Wasserstein norm as well. The results are then illustrated for N(n; k1, k2) and k-runs statistics.
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تاریخ انتشار 2014