Knowledge concerning the family of univariate continuous distributions with density function f and distribution function F defined through the relation f(x) = F (x)(1 − F (x)), α, β ∈ R, is reviewed and modestly extended. Symmetry, modality, tail behaviour, order statistics, shape properties based on the mode, L-moments and — for the first time — transformations between members of the family ar...

Percolation is one of the most studied processes in statistical physics. A recent paper by Achlioptas [Science 323, 1453 (2009)] showed that the percolation transition, which is usually continuous, becomes discontinuous ("explosive") if links are added to the system according to special cooperative rules (Achlioptas processes). In this paper, we present a detailed numerical analysis of Achliopt...

In prefix coding over an infinite alphabet, methods that consider specific distributions generally consider those that decline more quickly than a power law (e.g., Golomb coding). Particular power-law distributions, however, model many random variables encountered in practice. For such random variables, compression performance is judged via estimates of expected bits per input symbol. This corr...

Pronunciation time probability density and hazard functions from large speeded word naming data sets were assessed for empirical patterns consistent with multiplicative and reciprocal feedback dynamics - interaction dominant dynamics. Lognormal and inverse power law distributions are associated with multiplicative and interdependent dynamics in many natural systems. Mixtures of lognormal and in...