Non-Gaussian Error Distributions of Galactic Rotation Speed Measurements

TL;DR

This paper analyzes the error distributions of galactic rotation speed measurements, revealing non-Gaussian characteristics and proposing the median as a robust central estimate due to the heavy tails in the data.

Contribution

It constructs and compares error distributions for $ heta_0$, demonstrating non-Gaussianity and identifying the Student's t-distribution as the best fit, recommending the median as the central estimate.

Findings

Error distributions have wider tails than Gaussian.

Student's t-distribution with n=2 fits best.

Median value of 219.65 km/sec recommended as central estimate.

Abstract

We construct the error distributions for the galactic rotation speed ($\Theta_0$) using 137 data points from measurements compiled in De Grijs et al. (arXiv:1709.02501), with all observations normalized to the galactocentric distance of 8.3 kpc. We then checked (using the same procedures as in works by Ratra et al) if the errors constructed using the weighted mean and the median as the estimate, obey Gaussian statistics. We find using both these estimates that they have much wider tails than a Gaussian distribution. We also tried to fit the data to three other distributions: Cauchy, double-exponential, and Students-t. The best fit is obtained using the Students-$t$ distribution for $n=2$ using the median value as the central estimate, corresponding to a $p$-value of 0.1. We also calculate the median value of $\Theta_0$ using all the data as well as using the median of each set of measurements based on the tracer population used. Because of the non-gaussianity of the residuals, we point out that the subgroup median value, given by $\Theta_{med}=219.65$ km/sec should be used as the central estimate for $\Theta_0$.