The Spectral Index Distribution and Spectral Shape of the Unresolved Emission of GeV Blazars: Prospects for GLAST

We present a method for determining the parameters of an intrinsic spectral index distribution (ISID) of a class of gamma-ray emitters while accounting for error in measurement of the spectral indices of these emitters. We apply this method to the set of confident blazars from the Energetic Gamma-ray Experiment Telescope (EGRET) and a set of simulated Gamma-ray Large Area Space Telescope (GLAST) blazars. We find that the maximum likelihood ISID for EGRET blazars has a mean spectral index of 2.27 and a standard deviation of 0.20. We also test for spectral index hardening associated with blazar variability finding no evidence for such a phenomenon. Finally, we calculate the unabsorbed spectral shape of the blazar contribution to the extra- galactic gamma-ray background (EGRB) using the derived ISID, finding a (relatively) mildly convex, though not very well constrained, spectrum.