When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law, also known variously as Zipf’s law or the Pareto distribution. Power laws appear widely in physics, biology, earth and planetary sciences, economics and finance, computer science, demography and the social sciences. For instance, the distri...

A power law (PL) is the form taken by a large number of surprising empirical regularities in economics and finance. This review surveys well-documented empirical PLs regarding income and wealth, the size of cities and firms, stock market returns, trading volume, international trade, and executive pay. It reviews detailindependent theoretical motivations that make sharp predictions concerning th...

Heavy-tailed or power-law distributions are becoming increasingly common in biological literature. A wide range of biological data has been fitted to distributions with heavy tails. Many of these studies use simple fitting methods to find the parameters in the distribution, which can give highly misleading results. The potential pitfalls that can occur when using these methods are pointed out, ...

The notion that human learning follows a smooth power law (PL) of diminishing gains is well-established in psychology. This characteristic is observed when multiple curves are averaged, potentially masking more complex dynamics underpinning the curves of individual learners. Here, we analyzed 25,280 individual learning curves, each comprising 500 measurements of cognitive performance taken from...

What distribution of graphical degree sequence is invariant under “scaling”? Are these graphs always power-law graphs? We show the answer is a surprising “yes” for sparse graphs if we ignore isolated vertices, or more generally, the vertices with degrees less than a fixed constant k. We obtain a concentration result on the degree sequence of a random induced subgraph. The case of hypergraphs (o...

It is has been previously demonstrated [4] that Internet topologies which were once considered unstructured networks with no global design processes actually follow powerlaws, both at the router level and the AS (Autonomous System) domain level. This discovery has very wide implications on network research as well as network and protocol design. The Internet is not the only network instance to ...

Many empirical size distributions in economics and elsewhere exhibit power-law behaviour in the upper tail. This article contains a simple explanation for this. It also predicts lower-tail powerlaw behaviour, which is verified empirically for income and city-size data.

Acknowledgment During my PhD course I have been working as a part of a wide group, whose main research topics have been and still are located in the field of Software Engineering, with a special interest and attention to the Agile Methodolo-gies and to the software systems and processes modeling. My work, study and research activities have been always related to the work, study and research act...

The distribution of many real discrete random variables (e.g., the frequency of words, the population of cities) can be approximated by a zeta distribution, that is known popularly as Zipf’s law, or power law in physics. Here we revisit the relationship between power law distribution of a magnitude and the corresponding power relationship between the magnitude of a certain element and its rank....

A diagnostic of a power law distribution is that a log-log plot of frequency against rank yields a (nearly) straight line. For instance, Zipf (1935) plotted word token counts in a variety of texts against the inverse rank of each distinct word type and showed that typically such plots approximate a straight line. The characteristic ‘Zipf curve’ of word frequency against rank deviates from this ...