Non-Gaussian Error Distributions of LMC Distance Moduli Measurements

Understand

We construct error distributions for a compilation of 232 Large Magellanic Cloud (LMC) distance moduli values from de Grijs (2014) that give an LMC distance modulus of (m-M)_{0}=18.49 plus/minus 0.13 mag (median and 1 sigma symmetrized error).

• Central estimates found from weighted mean and median statistics are used to construct the error distributions.
• The weighted mean error distribution is non-Gaussian --- flatter and broader than Gaussian --- with more (less) probability in the tails (center) than is predicted by a Gaussian distribution; this could be the consequence of unaccounted-for systematic uncertainties.
• The median statistics error distribution, which does not make use of the individual measurement errors, is also non-Gaussian --- more peaked than Gaussian --- with less (more) probability in the tails (center) than is predicted by a Gaussian distribution; this could be the consequence of publication bias and/or the non-independence of the measurements.