We have translated fractional Brownian motion (FBM) signals into a text based on two ”letters”, as if the signal fluctuations correspond to a constant stepsize random walk. We have applied the Zipf method to extract the ζ′ exponent relating the word frequency and its rank on a loglog plot. We have studied the variation of the Zipf exponent(s) giving the relationship between the frequency of occ...

We present in this paper a numerical investigation of literary texts by various well-known English writers, covering the first half of the twentieth century, based upon the results obtained through corpus analysis of the texts. A fractal power law is obtained for the lexical wealth defined as the ratio between the number of different words and the total number of words of a given text. By consi...

Pareto, Zipf and numerous subsequent investigators of inverse power distributions have often represented their findings as though their data conformed to a power law form for all ranges of the variable of interest. I refer to this ideal case as a strong inverse power law (SIPL). However, many of the examples used by Pareto and Zipf, as well as others who have followed them, have been truncated ...

Motivated by the method of interpolating inequalities that makes use of the improved Jensen-type inequalities, in this paper we integrate this approach with the well known Zipf-Mandelbrot law applied to various types of f-divergences and distances, such are Kullback-Leibler divergence, Hellinger distance, Bhattacharyya distance (via coefficient), [Formula: see text]-divergence, total variation ...

We investigate the fluctuation behaviors of financial stock markets by Zipf analysis. In the present paper, the empirical research is made to describe ensembles and specifics of stock price returns for global stock indices, and the corresponding Zipf distributions are given. First we study the fluctuation behavior of global stock markets by m, k -Zipf method. Then we consider a dynamic stock pr...

In this article, we consider Zipf-Mandelbrot law as applied to texts in natural languages. We present a simple model of dependence of the law on the text size, which is featured by variable power-law tail and constant ratio of the most frequent words. As a result we derive several closed formulas, which accord with empirical data qualitatively and partially quantitatively. For example, there ap...

For words, rank-frequency distributions have long been heralded for adherence to a potentiallyuniversal phenomenon known as Zipf’s law. The hypothetical form of this empirical phenomenon was refined by Ben̂ıot Mandelbrot to that which is presently referred to as the Zipf-Mandelbrot law. Parallel to this, Herbert Simon proposed a selection model potentially explaining Zipf’s law. However, a signi...

In this article, we explore two approaches to modeling hypermedia-based communication. It is argued that the classical conveyor-tube framework is not applicable to the case of computerand Internetmediated communication. We then present a simple but very general system-theoretic model of the communication process, propose its mathematical interpretation, and derive several formulas, which qualit...