Co-occurrence of the Benford-like and Zipf Laws Arising from the Texts Representing Human and Artificial Languages

Abstract

We demonstrate that large texts, representing human (English, Russian, Ukrainian) and artificial (C++, Java) languages, display quantitative patterns characterized by the Benford-like and Zipf laws. The frequency of a word following the Zipf law is inversely proportional to its rank, whereas the total numbers of a certain word appearing in the text generate the uneven Benford-like distribution of leading numbers. Excluding the most popular words essentially improves the correlation of actual textual data with the Zipfian distribution, whereas the Benford distribution of leading numbers (arising from the overall amount of a certain word) is insensitive to the same elimination procedure. The calculated values of the moduli of slopes of double logarithmical plots for artificial languages (C++, Java) are markedly larger than those for human ones.