Cosmology-Independent Distance Moduli of 42 Gamma-Ray Bursts between   Redshift of 1.44 and 6.60
  This report is an update and extension of our paper accepted for publication in ApJ (arXiv:0802.4262). Since objects at the same redshift should have the same luminosity distance and the distance moduli of type Ia supernovae (SNe Ia) obtained directly from observations are completely cosmology independent, we obtain the distance modulus of a gamma-ray burst (GRB) at a given redshift by interpolating or iterating from the Hubble diagram of SNe Ia. Then we calibrate five GRB relations without assuming a particular cosmological model, from different regression methods, and construct the GRB Hubble diagram to constrain cosmological parameters. Based upon these relations we list the cosmology-independent distance moduli of 42 GRBs between redshift of 1.44 and 6.60, with the 1-$\sigma$ uncertainties of 1-3%. 
Nan Liang and Shuang Nan Zhang