The radio and gamma-ray luminosities of blazars

Based on the gamma -ray data of blazars in the third EGRET catalog and radi o data at 5 GHz, we studied the correlation between the radio and gamma -ta y luminosities using two statistical methods. The first method was the part ial correlation analysis method, which indicates that there e?;ist correlat ions between the radio and gamma -ray luminosities in both high and low sta tes as well as in the average case. The second method involved a comparison of expected gamma -ray luminosity distribution with the observed data usin g the Kolmogorov-Smirnov (KS) test. In the second method, we assumed that t here is a correlation between the radio and gamma -ray luminosities and tha t the gamma -ray luminosity function is proportional to the radio luminosit y function. The KS test indicates that the expected gamma-ray luminosity di stributions are consistent with the observed data in a reasonable parameter range. Finally, we used different gamma -ray luminosity functions to estim ate the possible 'observed' gamma -ray luminosity distributions by GLAST.