Beyond Zipf's Law: The Lavalette Rank Function and Its Properties
Por:
Fontanelli, Oscar, Miramontes, Pedro, Yang, Yaning, Cocho, Germinal, Li, Wentian
Publicada:
22 sep 2016
Resumen:
Although Zipf's law is widespread in natural and social data, one often
encounters situations where one or both ends of the ranked data deviate
from the power-law function. Previously we proposed the Beta rank
function to improve the fitting of data which does not follow a perfect
Zipf's law. Here we show that when the two parameters in the Beta rank
function have the same value, the Lavalette rank function, the
probability density function can be derived analytically. We also show
both computationally and analytically that Lavalette distribution is
approximately equal, though not identical, to the lognormal
distribution. We illustrate the utility of Lavalette rank function in
several datasets. We also address three analysis issues on the
statistical testing of Lavalette fitting function, comparison between
Zipf's law and lognormal distribution through Lavalette function, and
comparison between lognormal distribution and Lavalette distribution.
Filiaciones:
Fontanelli, Oscar:
Univ Nacl Autonoma Mexico, Fac Ciencias, Dept Matemat, Mexico City, DF, Mexico
Miramontes, Pedro:
Univ Nacl Autonoma Mexico, Fac Ciencias, Dept Matemat, Mexico City, DF, Mexico
Univ Leipzig, Bioinformat Grp, Leipzig, Germany
Univ Leipzig, Interdisciplinary Ctr Bioinformat, Leipzig, Germany
Yang, Yaning:
Univ Sci & Technol China, Dept Stat & Finance, Hefei, Anhui, Peoples R China
Cocho, Germinal:
Univ Nacl Autonoma Mexico, Inst Fis, Mexico City, DF, Mexico
Li, Wentian:
Northwell Hlth, Feinstein Inst Med Res, Robert S Boas Ctr Genom & Human Genet, Manhasset, NY USA
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