Koen, ChrisKondlo, L2013-12-022013-12-022009Koen, C. & Kondlo, L. (2009). Fitting power-law distributions to data with measurement errors. Monthly Notices of the Royal Astronomical Society, 397(1): 495-5050035-8711http://hdl.handle.net/10566/894If X, which follows a power-law distribution, is observed subject to Gaussian measurement error e, thenX+e is distributed as the convolution of the power-lawand 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 HI cloud masses in the LMC.en© 2009 copyright Oxford University Press. This file may be freely used for educational purposes, as long as it is not altered in any way. Acknowledgement of the authors and the source is required.Methods: statisticalISM: cloudsGalaxies: ISMArticle