Earthquake hazard parameters are estimated by the application of the maximu
m likelihood method. The technique is based on a procedure which utilizes d
ata of different quality, e.g., those in which the uncertainty in the asses
sment of the magnitudes is great and those in which the magnitudes are comp
uted with great precision. In other words the data were extracted from both
historical (incomplete) and recorded (complete) files. The historical part
of the catalogue contains only the strongest events, whereas the complete
part can be divided into several sub-catalogues; each one assumed to be com
plete above a specified magnitude threshold. Uncertainty in the determinati
on of magnitudes has also been taken into account. The method allows us to
estimate the earthquake hazard parameters which are the maximum regional ma
gnitude, M-max, the activity rate, gimel, of the seismic events and the wel
l known value beta (b = beta log e), which is the slope of the magnitude-fr
equency relationship. All these parameters are of physical significance. Th
e mean return periods, RP, of earthquakes with a certain lower magnitude M
greater than or equal to m are also determined. The method is applied in th
e Island of Crete and the adjacent area, where catastrophic earthquakes are
known from the historical era. The earthquake hazard of the whole area is
divided in a cellular manner which allow the analysis of the localized haza
rd parameters and the representation of their regional variation. The seism
ic hazard analysis, which is expressed by: (a) The annual probability of ex
ceedance of a specified value of magnitude and (b) the return periods (in y
ears) that are expected for given magnitudes, for shallow events is finally
performed for shallow events. This hazard analysis is useful for both theo
retical and practical reasons and provides a tool for earthquake resistant
design in both areas of low and high seismicity.