The cross-sectional distribution of government debt is often approximated by a lognormal distribution. This note empirically demonstrates that government debt is more accurately characterized by the double Pareto-lognormal (dPLN) distribution, which features a lognormal body with two Pareto tails. The dPLN assuredly surpasses alternative parametric distributions and passes goodness-of-fit tests. With its analytical tractability, flexibility, and parsimony, coupled with a theoretical foundation, the dPLN may be appealing for different computational and empirical applications.

Empirical studies of data traffic in high-speed networks suggest that network traffic exhibits self-similarity and long-range dependence. Cumulative network traffic has been modeled using the so-called ON/OFF model. It was shown that cumulative network traffic can be approximated by either fractional Brownian motion or stable Lévy motion, depending on how many sources are active in the model. In this paper we consider exceedances of a high threshold by the sequence of lengths of ON-periods. If the cumulative network traffic converges to stable Lévy motion, the number of exceedances converges to a Poisson limit. The same holds in the fractional Brownian motion case, provided a very high threshold is used. Finally, we show that the number of exceedances obeys the central limit theorem.