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Zipfs law describes the empirical size distribution of the components of many systems in natural and social sciences and humanities. We show, by solving a statistical model, that Zipfs law co-occurs with the maximization of the diversity of the component sizes. The law ruling the increase of such diversity with the total dimension of the system is derived and its relation with Heaps law is discussed. As an example, we show that our analytical results compare very well with linguistics datasets.
This paper investigates the rank distribution, cumulative probability, and probability density of price returns for the stocks traded in the KSE and the KOSDAQ market. This research demonstrates that the rank distribution is consistent approximately
The origin(s) of the ubiquity of Zipfs law (an inverse power law form for the probability density function (PDF) with exponent $1+1$) is still a matter of fascination and investigation in many scientific fields from linguistic, social, economic, comp
A major problem for evolutionary theory is understanding the so called {em open-ended} nature of evolutionary change, from its definition to its origins. Open-ended evolution (OEE) refers to the unbounded increase in complexity that seems to characte
We statistically investigate the distribution of share price and the distributions of three common financial indicators using data from approximately 8,000 companies publicly listed worldwide for the period 2004-2013. We find that the distribution of
We propose hypotheses describing the empirical finding of an association between the exponents of urban GDP scaling and Zipfs law for cities. These hypotheses represent various combinations of directional or reciprocal causal links between the two ph