Acta Applicandae Mathematicae 00: 1–13, 2003. © 2003 Kluwer Academic Publishers. Printed in the Netherlands. 1 A New Estimator for a Tail Index V. PAULAUSKAS Department of Mathematics and Informatics, Vilnius University and Institue of Mathematics and Informatics, Akademijos 4, LT-2021 Vilnius, Lithuania (Received: 31 August 2002) Abstract. We investigate properties of a new estimator for a tail index introduced by Davydov and co-workers. The main advantage of this estimator is the simplicity of the statistic used for the estimator. We provide results of simulation by comparing plots of our’s and Hill’s estimators. Mathematics Subject Classifications (1991): Key words: 1. Introduction and Formulation of Results During past few decades, in many fields of applied probability, more and more attention has been paid to heavy-tailed distributions and, as a consequence, the problem of estimation of a tail index from various types of data has become rather important. At present, there are several known estimators, all of them expressed as some functionals of order statistics of a sample, the best known among them being the one proposed by Hill in [15]. Let us consider a sample of size n taken from a heavy-tailed distribution func- tion F , that is, we assume that X 1 ,...,X n are independent identically distributed (i.i.d.) random variables with a distribution function F satisfying the following relation for large x : 1 − F(x) = x −α L(x), (1) where α> 0, and L is slowly varying: lim x →∞ L(tx) L(x) = 1. Let X n,1  X n,2  ···  X n,n denote the order staistics of X 1 ,...,X n . The following estimator to estimate the parameter γ = 1/α was proposed in [15]: γ (1) n,k = 1 k k−1  i =0 log X n,n−i − log X n,n−k , where k is some number satisfying 1  k  n. The problem of how to choose k is rather complicated (see, for example, [4, 10, 11, 13, 14, 16]). During the 25 years acapvil38.tex; 16/07/2003; 15:06; p.1 VTEX(lina) pips. no.: 5127059 artty:res(acapkap:mathfam) v.1.2