Non-Gaussian error distributions of galactic rotation speed measurements

Abstract

We construct the error distributions for the galactic rotation speed (Θ0) using 137 data points from measurements compiled in De Grijs et al. [1], 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 Θ0 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 Θ med = 219.65 km/sec should be used as the central estimate for Θ0.

Median Statistics Estimate of the Distance to M87

“…However, we determine that the full compilation, as well as the two sub-compilations studied by deGB are significantly non-Gaussian. 5 Non-Gaussian data compilations are not uncommon in astronomy: well known examples including Hubble constant measurements (Gott et al 2001;Chen & Ratra 2011;Calabrese et al 2012;Bethapudi & Desai 2017;Zhang 2018), cosmological mass density estimates , distances to the SMC and LMC (De Grijs et al 2014;, and measurements of the Solar radius and Galactic rotational velocity (De Grijs & Bono 2016Camarillo et al 2018aCamarillo et al , 2018bRajan & Desai 2018;Bobylev & Bajkova 2021).…”

MFV approach to robust estimate of neutron lifetime

“…The conventional median technique is one of the most widely used statistical procedures to estimate the characteristics of different observational quantities in many statistical applications because it is not sensitive to outliers [11]. There have been a number of known examples of non-Gaussian data [12] to apply the median statistics, involving Hubble constant [13,14], 7 Li abundance [15,16], LMC and SMC distance [17], deuterium abundance and spatial curvature constraints [18], the distance to the Galactic center [19], galactic rotational velocity [20,21] and Newton's constants [22]. Recently, Rajan and Desai [23] investigated the measurements of neutron lifetime tabulated by Tanabashi et al from Particle Data Group (PDG, hereafter, the 2019 edition) [24] based on a meta analysis.…”

Gaussian Processes, Median Statistics, Milky Way Rotation Curves

“…Of course, since median statistics does not make use of the quoted error bars, the median statistics constraints will be less precise than the weighted mean ones, but probably more accurate. 2 Examples include Hubble constant measurements ; Chen & Ratra 2011a; Zhang 2018), 7 Li and D primordial abundance measurements Zhang 2017;Zavarygin et al 2018;Penton et al 2018), LMC and SMC distance moduli measurements (de Grijs et al 2014;, and parameters of the Milky Way (de Grijs & Bono 2016Rajan & Desai 2018b;Camarillo et al 2018a,b). For other examples see Bailey (2017) and Rajan & Desai (2018a).…”