Fitting power-law distributions to data with measurement errors

Abstract

If X, which follows a power-law distribution, is observed subject to Gaussian measurement
\nerror e, thenX+e is distributed as the convolution of the power-lawand Gaussian distributions.
\nMaximum-likelihood estimation of the parameters of the two distributions is considered.
\nLarge-sample formulae are given for the covariance matrix of the estimated parameters, and
\nimplementation of a small-sample method (the jackknife) is also described. Other topics dealt
\nwith are tests for goodness of fit of the posited distribution, and tests whether special cases (no
\nmeasurement errors or an infinite upper limit to the power-law distribution) may be preferred.
\nThe application of the methodology is illustrated by fitting convolved distributions to masses
\nof giant molecular clouds in M33 and the Large Magellanic Cloud (LMC), and to HI cloud
\nmasses in the LMC.