Journal of statistical planning and inference vol:45 issue:1-2 pages:21-48
The limit behaviour of the mean residual life function of a distribution gives important information on the tail of that distribution. In this paper this is shown through new Abelian-and Tauberian-type results on the transform linking both distribution function and mean residual life function. We use these analytic results to derive tail heaviness and extreme quantile estimators. Some basic asymptotic results for these estimators are given.