Most Frequent Value Statistics and the Hubble Constant

The measurement of Hubble constant (H0) 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 H0, regardless of the Gaussian or non-Gaussian distributions. The updated data set of H0 contains the 591 measurements including the extensive compilations of Huchra and other researchers. The calculated result of the MFV is H0 = 67.498 km s−1 Mpc−1, which is very close to the average value of recent Planck H0 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 H0 under different conditions, and find that the 95% confidence interval for the MFV of H0 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.