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 omega is measured for a given ''text'' (sequence of digits). In the case of various non-Marko vian sequences, the probability density of the frequencies P(omega) ha s a power-law tail. Here we argue that a broad class of unbiased binar y texts exhibiting a nonexponential distribution of cluster sizes can indeed yield a power-law behavior of P(omega), where we define cluster s to be strings of identical digits. We support this result by numeric al studies of long-range correlated sequences generated by three diffe rent methods that result in nonexponential cluster-size distribution: inverse Fourier transformation, Levy walks, and the expansion-modifica tion system. Our calculations shed light on the possible connection be tween the Zipf plot and the non-Markovian nature of the text: as the l ong-range correlations become dominant, the probability of the appeara nce of long clusters is increased, leading to the observed ''scaling'' in the Zipf plot.