NON-GAUSSIAN ERROR DISTRIBUTIONS OF LMC DISTANCE MODULI MEASUREMENTS

Abstract

We construct error distributions for a compilation of 232 Large Magellanic\nCloud (LMC) distance moduli values from de Grijs (2014) that give an LMC\ndistance modulus of (m-M)_{0}=18.49 plus/minus 0.13 mag (median and 1 sigma\nsymmetrized error). Central estimates found from weighted mean and median\nstatistics are used to construct the error distributions. The weighted mean\nerror distribution is non-Gaussian --- flatter and broader than Gaussian ---\nwith more (less) probability in the tails (center) than is predicted by a\nGaussian distribution; this could be the consequence of unaccounted-for\nsystematic uncertainties. The median statistics error distribution, which does\nnot make use of the individual measurement errors, is also non-Gaussian ---\nmore peaked than Gaussian --- with less (more) probability in the tails\n(center) than is predicted by a Gaussian distribution; this could be the\nconsequence of publication bias and/or the non-independence of the\nmeasurements. We also construct the error distributions of 247 SMC distance\nmoduli values from de Grijs (2015). We find a central estimate of\n(m-M)_{0}=18.94 plus/minus 0.14 mag (median and 1 sigma symmetrized error), and\nsimilar probabilities for the error distributions.\n