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The normal inverse Gaussian (NIG) distribution has previously been shown to be a versatile tool to model heavy-tailed processes. A cumulant-matching estimator of the NIG parameters was introduced in Oigard and Hansen (2001). Here, we analyze the performance of this estimator. Next, we study whether NIG models are appropriate models for multi-user interference. Finally, we empirically test the goodness of fit of squared-NIG models to tele-traffic data, which have been fitted with alpha-stable models.