Abstract
This appendix summarizes the mathematical details of the arguments presented in the main text. As this summary is brief, readers who would like a more thorough presentation should refer to the corresponding textbooks and original papers cited below.
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Notes
- 1.
Note that when g is an exponential function, as in Chap. 7, it is fitted by taking the logarithm only for y.
References
Clauset, Aaron, Shalizi, Cosma R., and Newman, Mark E. J. (2009). Power-law distributions in empirical data. SIAM review, 51(4), 661–703.
Cover, Thomas M. and Thomas, Joy A. (1991). Elements of Information Theory. John Wiley & Sons, Inc.
Lü, Linyuan, Zhang, Zi-Ke, and Zhou, Tao (2010). Zipf’s law leads to Heaps’ law : Analyzing their relation in finite-size systems. PLoS ONE, 5(12):e14139.
Mandelbrot, Benoit B. (1965). Information Theory and Psycholinguistics. Scientific Psychology, pages 250—368.
Manning, Christopher D. and Schütze, Hinrich (1999). Foundations of Statistical Natural Language Processing. The MIT Press.
Miller, George A. (1957). Some effects of intermittent silence. The American Journal of Psychology, 70(2), 311–314.
Mitzenmacher, Michael (2003). A brief history of generative models for power law and lognormal distributions. Internet Mathematics, 1(2), 226–251.
Moradi, Hamid, Grzymala-Busse, Jerzy W., and Roberts, James A. (1998). Entropy of English text: Experiments with humans and a machine learning system based on rough sets. Information Sciences, 104, 31–47.
Rényi, Alfréd (1961). On measures of entropy and information. Proceedings of the Fourth Berkeley Symposium on Mathematics, Statistics and Probability, pages 547–561.
Shannon, Claude E. (1951). Prediction and entropy of printed English. The Bell System Technical Journal, 30, 50–64.
Tanaka-Ishii, Kumiko and Aihara, Shunsuke (2015). Computational constancy measures of texts: Yule’s K and Rényi’s entropy. Computational Linguistics, 41, 481–502.
Tian, Ran, Okazaki, Naoyuki, and Inui, Kentaro (2017). The mechanism of additive composition. Machine Learning, 106(7), 1083–1130.
Tsallis, Constantino (1988). Possible generalization of Boltzmann-Gibbs statistics. Journal of Statistical Physics, 52(1–2), 479–487.
Yule, George Udny (1944). The Statistical Study of Literary Vocabulary. Cambridge University Press.
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Tanaka-Ishii, K. (2021). Mathematical Details. In: Statistical Universals of Language. Mathematics in Mind. Springer, Cham. https://doi.org/10.1007/978-3-030-59377-3_21
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