  The maximum product of spacings (MPS) is employed in the estimation of the
Generalized Extreme Value Distribution (GEV) and the Generalized Pareto
Distribution (GPD). Efficient estimators are obtained by the MPS for all
$\gamma$. This outperforms the maximum likelihood method which is only valid
for $\gamma<1$. It is then shown that the MPS gives estimators closer to the
true parameters compared to the maximum likelihood estimates (MLE) in a
simulation study. In cases where sample sizes are small, the MPS performs
stably while the MLE does not. The performance of MPS estimators is also more
stable than those of the probability-weighted moment (PWM) estimators. Finally,
as a by-product of the MPS, a goodness of fit statistic, Moran's statistic, is
available for the extreme value distributions. Empirical significance levels of
Moran's statistic calculated are found to be satisfactory with the desired
level.
