Abstract
In an insurance context, consider {Xn, n¡Ý1} random claim sizes with common distribution function F and {N(t), t ¡Ý0} an integer valued stochastic process that counts the number of claims occurring during the time interval [0, t). Based on the number of near-extremes which are the observations Xi near the largest or the m-th largest observation we derive in this paper a strongly consistent estimator of upper tails of X1-. Further, estimators for both the tail index and the upper endpoint are introduced when F is a generalised Pareto distribution. Asymptotic normal law for the proposed estimators is additionally presented.
Keywords: Number of near-extremes, Generalised Pareto Distribution, estimation of tail index, estimation of the upper endpoint, asymptotic normality.
Volume
Berlin
Year
2003
Categories
Financial and Statistical Methods
Loss Distributions
Extreme Values
Publications
ASTIN Colloquium
