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The same relationship occurs in many other rankings unrelated to language, such as the population ranks of cities in various countries, corporation sizes, income rankings, ranks of number of people watching the same TV channel,  and so on. This page was last changed on 19 Octoberat The law is named after the American linguist George Kingsley Zipf —who popularized it and sought to explain it Zipf, though he did not claim to have originated it.
The same relationship occurs in many other rankings, unrelated to language, such as the population ranks of cities in various countries, corporation sizes, income rankings, etc. It was originally derived to explain population versus rank in species by Yule, and applied to cities by Simon.
The connecting lines do not indicate continuity. He took a large class of well-behaved statistical distributions not only the normal distribution and expressed them in terms of rank. In other projects Wikimedia Commons. The tail frequencies of the Yule—Simon distribution are approximately. The law is named after the linguist George Kingsley Zipfwho first proposed ee. Only vocabulary items are needed to account for half the Brown Corpus.
Discrete distributions Computational linguistics Power laws Statistical laws Empirical laws Tails of probability distributions Quantitative linguistics Bibliometrics Corpus linguistics introductions.
However, this cannot hold exactly, because items must occur an integer number of times; there cannot be 2. In practice, as easily observable in distribution plots for large corpora, the observed distribution can be modelled more accurately as a sum of separate distributions for different subsets or subtypes of words that follow different parameterizations of the Zipf—Mandelbrot distribution, in particular the closed class of functional words exhibit s lower than 1, while dd vocabulary growth with document size and corpus size require s greater than 1 for convergence of the Generalized Harmonic Series.
The appearance of the distribution in rankings of cities by population was first noticed by Felix Auerbach in This can markedly improve the fit over a simple power-law relationship. Human behavior and the principle of least effort.
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