A Possible Origin of Power-Law Behavior in n-Tuple Zipf Analysis

In n-tuple Zipf analysis, ‘‘words’’ are defined as strings of n digits, and their normalized frequency of occurrence v is measured for a given ‘‘text’’ ~sequence of digits!. In the case of various non-Markovian sequences, the probability density of the frequencies P(v) 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 P(v), 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 expansionmodification 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. @S1063651X~96!08006-3#