Beyond Zipf's Law: The Lavalette Rank Function and Its Properties

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 l...

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Bibliographic Details
Published in:PloS one 2016-09, Vol.11 (9), p.e0163241-e0163241
Main Authors: Fontanelli, Oscar, Miramontes, Pedro, Yang, Yaning, Cocho, Germinal, Li, Wentian
Format: Article
Language:English
Subjects:
Bioinformatics
Biology and Life Sciences
Critical phenomena
Genomes
Mutation
Normal distribution
Physical Sciences
Power
Probability density function
Probability density functions
Research and Analysis Methods
Social Sciences
Statistical analysis
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Summary: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.
ISSN:1932-6203
1932-6203
DOI:10.1371/journal.pone.0163241