# 齊夫定律

參數 機率 mass 函數 Zipf PMF for N = 10 on a log-log scale. The horizontal axis is the index k . (Note that the function is only defined at integer values of k. The connecting lines do not indicate continuity.) 累積分布函數 Zipf CMF for N = 10. The horizontal axis is the index k . (Note that the function is only defined at integer values of k. The connecting lines do not indicate continuity.) $s>0\,$ (real) $N \in \{1,2,3\ldots\}$ (integer) $k \in \{1,2,\ldots,N\}$ $\frac{1/k^s}{H_{N,s}}$ $\frac{H_{k,s}}{H_{N,s}}$ {{{notation}}} $\frac{H_{N,s-1}}{H_{N,s}}$ $1\,$ $\frac{s}{H_{N,s}}\sum_{k=1}^N\frac{\ln(k)}{k^s} +\ln(H_{N,s})$ $\frac{1}{H_{N,s}}\sum_{n=1}^N \frac{e^{nt}}{n^s}$ $\frac{1}{H_{N,s}}\sum_{n=1}^N \frac{e^{int}}{n^s}$

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• George K. Zipf, Human Behaviour and the Principle of Least-Effort, Addison-Wesley, Cambridge MA, 1949
• W. Li, "Random texts exhibit Zipf's-law-like word frequency distribution", IEEE Transactions on Information Theory, 38(6), pp.1842-1845, 1992.
• Alexander Gelbukh, Grigori Sidorov. "Zipf and Heaps Laws’ Coefficients Depend on Language". Proc. CICLing-2001, Conference on Intelligent Text Processing and Computational Linguistics, 2001-02-18 ~ 02-24 Mexico City. Lecture Notes in Computer Science N 2004, ISSN 0302-9743, ISBN 3-540-41687-0, Springer-Verlag, pp. 332–335.
• Damian H. Zanette. Zipf's law and the creation of musical context. Online preprint at http://xxx.arxiv.org/abs/cs.CL/0406015
• Kali R. The city as a giant component: a random graph approach to Zipf's law. Applied Economics Letters, 2003-09-15, vol. 10, iss. 11, pp. 717-720(4)