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Zhang, Yifei; Shan, Shi; Yan, Chunning; Qiu, Junping; Xiong, Li (2016): Herdan-Heaps Law Corresponds to Lotka's Law: A Dynamic Perspective from Simon's Model. In: Journal of Quantitative Linguistics, Vol. 23, No. 2: pp. 211-227
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Abstract

Herdan-Heaps law and Lotka's law are two important laws in linguistics and many other fields, which are often found to coexist in many languages. Herdan-Heaps law describes the type-token relation between number of distinct words and text length. Lotka's law concerns the fraction of words with a given number of word occurrences. Utilising a variant of the Simon model, this work demonstrates that if the growth rate of different words follow Herdan-Heaps law, with an exponent in the interval (0,1), then the exponents of Lotka's law and Herdan-Heaps law are identical. A biparameter power law distribution, i.e. the Waring distribution, is derived within the framework of Simon's model. Estimators of the Waring distribution parameters are determined and numerical illustrations are provided.