The ionosphere can be characterized with its electron density distribution which is a complex function of spatial and temporal variations, geomagnetic, solar and seismic activity. An important measurable quantity about the electron density is the Total Electron Content (TEC) which is proportional to the total number of electrons on a line crossing the atmosphere. TEC measurements enable monitoring variations in the space weather. Global Positioning System (GPS) and the network of world-wide receivers provide a cost-effective solution in estimating TEC over a significant proportion of global land mass. In this study, five earthquakes between 2003-2008 that occurred in Japan with different seismic properties, and the China earthquake in play 2008 are investigated. The TEC data set is investigated by using the Kullback-Leibler Divergence (KLI), Kullback-Leibler Distance (KLD) and L2-Norm (L2N) which are used for the first time in the literature in this context and Cross Correlation Function (CCF) which is used in the literature before for quiet day period (QDP), disturbed day period (DDP), periods of IS days before a strong earthquake (BE) and after the earthquake (AE). In summary, it is observed that the CCF, KLD and L2N between the neighbouring GPS stations cannot be used as a definitive earthquake precursor due to the complicated nature of earthquakes and various uncontrolled parameters that effect the behavior of TEC such as distance to the earthquake epicenter, distance between the stations, depth of the earthquake, strength of the earthquake and tectonic structure of the earthquake. KLD, KLI and L2N are used for the first time in literature for the investigation of earthquake precursor for the first time in literature and the extensive study results indicate that for more reliable estimates further space-time TEC analysis is necessary over a denser GPS network in the earthquake zones.