Mobile Call Graphs: Beyond Power-Law and Lognormal Distributions, Mukund Seshadri, Sridhar Machiraju, Ashwin Sridharan, Jean Bolot, Christos Faloutsos, Jure Leskovec, Proc. of ACM KDD'08, August 2008, Las Vegas, NV.
This paper analyzes mobile phone calls data from the Sprint network and tries to create a model of the underlying graphs associated with different metrics: Partners (number of callers and callees associated with each user); calls (total number of calls made or received by a given user); duration (total duration of calls for each user). For each of these, the distribution has a power law tail, but a power law distribution does not fit well the rest of the distribution. The lognormal distribution fits better, except for the tail where it is off. So the paper considers the Double Pareto Log Normal (DPLN) distribution and explains how to find the best fit for that distribution.
This distribution would be useful for creating synthetic models to evaluate different social network parameters.