Non-Gaussian Error Distributions of LMC Distance Moduli Measurements

TL;DR

This study analyzes the error distributions of LMC and SMC distance measurements, revealing non-Gaussian characteristics likely due to systematic uncertainties, publication bias, or measurement dependencies, which impacts the understanding of their uncertainties.

Contribution

It constructs and compares non-Gaussian error distributions for LMC and SMC distance moduli, highlighting potential sources of deviations from Gaussian assumptions.

Findings

Weighted mean error distribution is flatter and broader than Gaussian.

Median error distribution is more peaked than Gaussian.

Error distributions suggest unaccounted systematic uncertainties and publication bias.

Abstract

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. We also construct the error distributions of 247 SMC distance moduli values from de Grijs (2015). We find a central estimate of (m-M)_{0}=18.94 plus/minus 0.14 mag (median and 1 sigma symmetrized error), and similar probabilities for the error distributions.