Random populations represented by stochastically scattered collections of real-valued points are abundant across many fields of science. Fractality, in the context of random populations, is conventionally associated with a Paretian distribution of the population's values.

The Lorenz curve is a universally calibrated statistical tool measuring quantitatively the distribution of wealth within human populations. We consider infinite random populations modeled by inhomogeneous Poisson processes defined on the positive half-line—the randomly scattered process-points...

We consider an evolving ensemble assembled from a set of n different elements via a stochastic growth process in which independent and identically distributed copies of the elements arrive randomly in time, and their statistics are governed by Zipf’s law. The associated “Heaps process” is...

Consider a finite sequence of independent–though not, necessarily, identically distributed–real-valued random scores. If the scores are absolutely continuous random variables, the sequence possesses a unique maximum (minimum). We say that “maximal (minimal) independence” holds if the...