Non-Gaussian Error Distribution of $\rm{^{7}Li}$ Abundance Measurements

Abstract

We construct the error distribution of $\rm{^{7}Li}$ abundance measurements for 66 observations (with error bars) used by Spite12 that give $\rm{A(Li)}=2.21 \pm 0.065$ (median and 1$\sigma$ symmetrized error). This error distribution is somewhat non-Gaussian, with larger probability in the tails than is predicted by a Gaussian distribution. The 95.4% confidence limits are 3.0$\sigma$ in terms of the quoted errors. We fit the data to four commonly used distributions: Gaussian, Cauchy, Student's t, and double exponential with the center of the distribution found with both weighted mean and median statistics. It is reasonably well described by a widened $n=8$ Student's $t$ distribution. Assuming Gaussianity, the observed A(Li) is 6.5$\sigma$ away from that expected from standard Big Bang nucleosynthesis given the $Planck$ observations Coc2014. Accounting for the non-Gaussianity of the observed A(Li) error distribution reduces the discrepancy to 4.9$\sigma$, which is still significant.