  In an earthquake event, the combination of a strong mainshock and damaging
aftershocks is often the cause of severe structural damages and/or high death
tolls. The objective of this paper is to provide estimation for the probability
of such extreme events where the mainshock and the largest aftershocks exceed
certain thresholds. Two approaches are illustrated and compared -- a parametric
approach based on previously observed stochastic laws in earthquake data, and a
non-parametric approach based on bivariate extreme value theory. We analyze the
earthquake data from the North Anatolian Fault Zone (NAFZ) in Turkey during
1965-2018 and show that the two approaches provide unifying results.
