Most Frequent Value Statistics and the Hubble Constant. (26th June 2018) - Zhang, J.
Abstract: The measurement of Hubble constant ( H 0 ) is clearly a very important task in astrophysics and cosmology. Based on the principle of minimization of the information loss, we propose a robust most frequent value (MFV) procedure to determine H 0, regardless of the Gaussian or non-Gaussian distributions. The updated data set of H 0 contains the 591 measurements including the extensive compilations of Huchra and other researchers. The calculated result of the MFV is H 0 = 67.498 km s −1 Mpc −1, which is very close to the average value of recent Planck H 0 value (67.81 ± 0.92 km s −1 Mpc −1 and 66.93 ± 0.62 km s −1 Mpc −1 ) and Dark Energy Survey Year 1 Results. Furthermore, we apply the bootstrap method to estimate the uncertainty of the MFV of H 0 under different conditions, and find that the 95% confidence interval for the MFV of H 0 measurements is [66.319, 68.690] associated with statistical bootstrap errors, while a systematically larger estimate is H 0 = 67.498 − 3.278 + 7.970 (systematic uncertainty). Especially, the non-Normality of error distribution is again verified via the empirical distribution function test including Shapiro–Wilk test and Anderson–Darling test. These results illustrate that the MFV algorithm has many advantages in the analysis of such statistical problems, no matter what the distributions of the original measurements are.