[R] how to fit a curve of form Y = X^Z

Philipp Pagel p.pagel at wzw.tum.de
Tue Jun 17 18:47:22 CEST 2008

> I have two variables X and Y, and think that Y is related
> to X by a function of the form : Y = X^Z, where Z is < 1. 
> However, I'm not sure how to find the best-fit equation to
> fit my data to a curve of this form using R. Have you any ideas?

You can use nlm() to fit a non-linear model. Another option
would be to fit a linear model to log-log transformed data.
However, if you are actually trying to fit to a power-law distribution
you may want to have a look at these references:

Goldstein, M.; Morris, S. & Yen, G. 
Problems with Fitting to the Power-Law Distribution 
European Physical Journal B, 2004, 41, 255-258

Newman, M. E. J. 
Power laws, Pareto distributions and Zipf's law
Contemporary Physics, 2005, 46, 323


Dr. Philipp Pagel
Lehrstuhl für Genomorientierte Bioinformatik
Technische Universität München
Wissenschaftszentrum Weihenstephan
85350 Freising, Germany

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