The Radio and Gamma-Ray Luminosities of Blazars
Based on the $γ$-ray data of blazars in the third EGRET catalog and radio data at 5 GHz, we studied the correlation between the radio and $γ$-ray luminosities using two statistical methods. The first method was the partial correlation analysis method, which indicates that there exist correlations between the radio and $γ$-ray luminosities in both high and low states as well as in the average case. The second method involved a comparison of expected $γ$-ray luminosity distribution with the observed data using the Kolmogorov-- Smirnov (KS) test. In the second method, we assumed that there is a correlation between the radio and $γ$-ray luminosities and that the $γ$-ray luminosity function is proportional to the radio luminosity function. The KS test indicates that the expected gamma-ray luminosity distributions are consistent with the observed data in a reasonable parameter range. Finally, we used different $γ$-ray luminosity functions to estimate the possible 'observed' $γ$-ray luminosity distributions by GLAST.