  Analysis of the rare and extreme values through statistical modeling is an
important issue in economical crises, climate forecasting, and risk management
of financial portfolios. Extreme value theory provides the probability models
needed for statistical modeling of the extreme values. There are generally two
ways to identifying the extreme values in a data set, the block-maxima and the
peak-over threshold method. The block-maxima method uses the Generalized
Extreme Value distribution and the peak-over threshold method uses the
Generalized Pareto distribution. It is common that the location of these
distributions kept fixed. It is possible that some unobserved variables produce
heterogeneity in the location of the assumed distribution. In this article we
focus on modeling this unobserved heterogeneity in block-maxima method.
