The Radio and Gamma-Ray Luminosi0074ies of Blazars

Based on the $\gamma$-ray data of blazars in the third EGRET catalog andradio data at 5 GHz, we studied the correlation between the radio and$\gamma$-ray luminosities using two statistical methods. The first method wasthe partial correlation analysis method, which indicates that there existcorrelations between the radio and $\gamma$-ray luminosities in both high andlow states as well as in the average case. The second method involved a comparison of expected $\gamma$-ray luminositydistribution with the observed data using the Kolmogorov-- Smirnov (KS) test. In the second method, we assumed that there is acorrelation between the radio and $\gamma$-ray luminosities and that the$\gamma$-ray luminosity function is proportional to the radio luminosityfunction. The KS test indicates that the expected gamma-ray luminositydistributions are consistent with the observed data in a reasonable parameterrange. Finally, we used different $\gamma$-ray luminosity functions to estimatethe possible 'observed' $\gamma$-ray luminosity distributions by GLAST.Comment: 8 pages, 4 figures, one table, PASJ, 53 (2001