Power law cumulative number-size distributions are widely used to describe the scaling properties of data sets and to establish scale invariance. We derive the relationships between the scaling exponents of non-cumulative and cumulative number-size distributions for linearly binned and logarithmically binned data. Cumulative number-size distributions for data sets of many natural phenomena exhi...

A theorem due to L. J. Gleser stating that a gamma distribution with shape parameter no greater than one is a mixed exponential distribution is extended to generalized gamma distributions introduced by E. W. Stacy as a special family of lifetime distributions containing both gamma distributions, exponential power and Weibull distributions. It is shown that the mixing distribution is a scale mix...

Studies of collective human behavior in the social sciences, often grounded in details of actions by individuals, have much to offer ‘social’ models from the physical sciences concerning elegant statistical regularities. Drawing on behavioral studies of social influence, we present a parsimonious, stochastic model, which generates an entire family of real-world rightskew socio-economic distribu...

Studies of collective human behaviour in the social sciences, often grounded in details of actions by individuals, have much to offer ‘social' models from the physical sciences concerning elegant statistical regularities. Drawing on behavioural studies of social influence, we present a parsimonious, stochastic model, which generates an entire family of real-world right-skew socio-economic distr...

Many complex systems have been modeled as networks. Examples of such systems that are of interest to cognitive psychologists include the mental lexicon for spoken word recognition and semantic memory. A frequent finding in such studies is that the frequency distribution of the number of connections for each node in the network follows a power law. This finding has been interpreted to mean that ...

Tail estimates are developed for power law probability distributions with exponential tempering, using a conditional maximum likelihood approach based on the upper order statistics. Tempered power law distributions are intermediate between heavy power-law tails and Laplace or exponential tails, and are sometimes called “semiheavy” tailed distributions. The estimation method is demonstrated on s...

A few years ago it was noticed that the distributions of gene-family sizes in fully-sequenced genomes follow power-law distributions [8, 6]. Since then different authors have shown that there is in fact a large array of genomic features that show power law distributions. Almost all of these concern the distributions of genomic features within a single genome. For instance, it is shown in [13] t...