Journal
MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY
Volume 397, Issue 1, Pages 495-505Publisher
OXFORD UNIV PRESS
DOI: 10.1111/j.1365-2966.2009.14956.x
Keywords
methods: statistical; ISM: clouds; galaxies: ISM
Categories
Funding
- Square Kilometre Array (SKA) South Africa
- South African National Research Foundation (NRF)
- University of the Western Cape
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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.
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