Journal Article

Fitting power-law distributions to data with measurement errors

C. Koen and L. Kondlo

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 397, issue 1, pages 495-505
Published in print July 2009 | ISSN: 0035-8711
Published online July 2009 | e-ISSN: 1365-2966 | DOI: http://dx.doi.org/10.1111/j.1365-2966.2009.14956.x
Fitting power-law distributions to data with measurement errors

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If X, which follows a power-law distribution, is observed subject to Gaussian measurement error e, then X+e is distributed as the convolution of the power-law and Gaussian distributions. Maximum-likelihood estimation of the parameters of the two distributions is considered. Large-sample formulae are given for the covariance matrix of the estimated parameters, and implementation of a small-sample method (the jackknife) is also described. Other topics dealt with are tests for goodness of fit of the posited distribution, and tests whether special cases (no measurement errors or an infinite upper limit to the power-law distribution) may be preferred. The application of the methodology is illustrated by fitting convolved distributions to masses of giant molecular clouds in M33 and the Large Magellanic Cloud (LMC), and to H i cloud masses in the LMC.

Keywords: methods: statistical; ISM: clouds; galaxies: ISM

Journal Article.  5027 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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