Distance determination by magnitude analysis of some open clusters with GAIA era and stellar luminosity function

In this work, we carry out by utilizing the distance equation with providing some basic descriptive statistics for both apparent and absolute magnitudes, the distances of some open clusters (i.e., Hyades, Pleiades, IC 2391, Koposov 12, Koposov 43, NGC 1348, NGC 2112, NGC 4337, SAI 24, and SAI 94) with the assumption that all members N are scattering around a mean absolute magnitude in a Gaussian distribution. Our numerical obtained results are in good agreement with previously calculated values. In the second part of the paper, we have calculated the luminosity function of Hyades open cluster by Salpeter's normalized function Ψ(M_V) due to frequency distribution function Φ(M_V), on this way, we have got a very significant relationship between them with absolute magnitudes M_V (i.e., the linear correlation coefficient ∼ 0.995), and the error analysis are also given.