Non-Gaussian Error Distributions of LMC Distance Moduli Measurements

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Abstract

We construct error distributions for a compilation of 232 Large Magellanic Cloud (LMC) distance moduli values from de Grijs et al. that give an LMC distance modulus of (m – M)0 = 18.49 ± 0.13 mag (median and 1σ 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 & Bono. We find a central estimate of {(m-M)}0=18.94+/- 0.14 mag (median and 1σ symmetrized error), and similar probabilities for the error distributions.

Author

Crandall, Sara; Ratra, Bharat

Journal

Astrophysical Journal Supplement Series

Paper Publication Date

December 2015

Paper Type

Astrostatistics