In [Formula Presented]-tuple Zipf analysis, "words" are defined as strings of [Formula Presented] digits, and their normalized frequency of occurrence [Formula Presented] is measured for a given "text" (sequence of digits). In the case of various non-Markovian sequences, the probability density of the frequencies [Formula Presented] has a power-law tail. Here we argue that a broad class of unbiased binary texts exhibiting a nonexponential distribution of cluster sizes can indeed yield a power-law behavior of [Formula Presented], where we define clusters to be strings of identical digits. We support this result by numerical studies of long-range correlated sequences generated by three different methods that result in nonexponential cluster-size distribution: inverse Fourier transformation, Lévy walks, and the expansion-modification system. Our calculations shed light on the possible connection between the Zipf plot and the non-Markovian nature of the text: as the long-range correlations become dominant, the probability of the appearance of long clusters is increased, leading to the observed "scaling" in the Zipf plot.
|Number of pages||5|
|Journal||Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics|
|Publication status||Published - Jan 1 1996|
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics