  We extend the setting of the right endpoint estimator introduced in Fraga
Alves and Neves (Statist. Sinica 24:1811--1835, 2014) to the broader class of
light-tailed distributions with finite endpoint, belonging to some domain of
attraction induced by the extreme value theorem. This stretch enables a general
estimator for the finite endpoint, which does not require estimation of the
(supposedly non-positive) extreme value index. A new testing procedure for
selecting max-domains of attraction also arises in connection with asymptotic
properties of the general endpoint estimator. The simulation study conveys that
the general endpoint estimator is a valuable complement to the most usual
endpoint estimators, particularly when the true extreme value index stays above
$-1/2$, embracing the most common cases in practical applications. An
illustration is provided via an extreme value analysis of supercentenarian
women data.
