The distance modulus, modbest [mag] is a weighted average between mod0 and modz (the weight are the inverse square of the estimated errors on each parameter).
The distance modulus is related to the luminosity distance, expressed in Mpd, through the relation: modbest = 5 log(DL) + 25
Note that in cosmology other distances can also be defined, the proper distance (based on the Hubble expansion), and the angular-diameter and comoving distances. A modulus based on a luminosity-distance, like modbest, is called a 'true distance modulus'.
modbest is used to derive the absolute magnitude mabs.