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A novel statistical model, the one-dimensional hyperbolic distribution, is proposed for network traffic activity. This includes the modelling of network traffic performance and descriptive parameters, organised as probability distribution functions of activity monitored during an observation window. This model promises accurate representation in a compact manner, of particular interest in statistical anomaly intrusion detection systems. The hyperbolic distribution has been tested in modelling several performance parameters in data traces of IP traffic collected from various actual network environments, including the campus LANs of the New Jersey Institute of Technology and the WAN of the Bergen County Cooperative Library Network System (BCCLNS), as well as simulated client-server LANs. By fitting the model parameters to the experimental data, it is shown that this analytic model performs significantly better than the models currently in common use, such as the Weibull, Pareto, normal and lognormal distributions.