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The distribution of frequency counts of distinct words by length in a languages vocabulary will be analyzed using two methods. The first, will look at the empirical distributions of several languages and derive a distribution that reasonably explains the number of distinct words as a function of length. We will be able to derive the frequency count, mean word length, and variance of word length based on the marginal probability of letters and spaces. The second, based on information theory, will demonstrate that the conditional entropies can also be used to estimate the frequency of distinct words of a given length in a language. In addition, it will be shown how these techniques can also be applied to estimate higher order entropies using vocabulary word length.
This note derives the various forms of entropy of systems subject to Olbert distributions (generalized Lorentzian probability distributions known as $kappa$-distributions) which are frequently observed particularly in high temperature plasmas. The ge
With such increasing popularity and availability of digital text data, authorships of digital texts can not be taken for granted due to the ease of copying and parsing. This paper presents a new text style analysis called natural frequency zoned word
A measure called Physical Complexity is established and calculated for a population of sequences, based on statistical physics, automata theory, and information theory. It is a measure of the quantity of information in an organisms genome. It is base
In a recent paper [textit{M. Cristelli, A. Zaccaria and L. Pietronero, Phys. Rev. E 85, 066108 (2012)}], Cristelli textit{et al.} analysed relation between skewness and kurtosis for complex dynamical systems and identified two power-law regimes of no
Social impacts and degrees of organization inherent to opinion formation for interacting agents on networks present interesting questions of general interest from physics to sociology. We present a quantitative analysis of a case implying an evolving