In this study, the relation between Total Electron Content (TEC) estimates obtained from GPS and the earthquakes is examined. Five earthquakes between 2003-2008 occured in Japan with different properties and China earthquake in May 2008 are chosen for the purpose. The 15-days period before and after the registered earthquakes are considered for the basis of this investigation. Also the TEC in computed for each GPS station for the time periods including Ionosphere quiet and disturbed days not without any serious earthquake in the region. For the statistical analysis, the cross correlation function (CC) which is used in the literature before, and the Kullback-Leibler Divergence (KLD) with L2-Norm (L2N) methods which are used for the first time in this context, are applied to the data sets. The computed values for CC, KLD and L2N are compared for both between different GPS stations where available and between consecutive days for the time periods in the data set. With CC analysis, the anomalies existed in the earthquake time intervals are also observed for the quiet days data set. For the earthquakes with scale larger than 6, the possibilities of generating an alarm signal is more likely with a future detailed comperative study of the estimated TEC nearby GPS station estimates in space and time.