ESTIMATION OF THE FINITE RIGHT ENDPOINT IN THE GUMBEL DOMAIN

A simple estimator for the finite right endpoint of a distribution function in the Gumbel max-domain of attraction is proposed. Large sample properties such as consistency and the asymptotic distribution are derived. A simulation study is presented.

[1]  S. Girard,et al.  Weibull tail-distributions revisited: a new look at some tail estimators , 2011 .

[2]  S. Girard,et al.  Estimating an endpoint with high-order moments , 2012 .

[3]  Peter Hall,et al.  On Estimating the Endpoint of a Distribution , 1982 .

[4]  Laurens de Haan,et al.  On regular variation and its application to the weak convergence of sample extremes , 1973 .

[5]  P. Hall,et al.  Estimating the end-point of a probability distribution using minimum-distance methods , 1999 .

[6]  L. Haan,et al.  Extreme value theory : an introduction , 2006 .

[7]  Fritz Scholz.  Statistical Extreme Value Analysis of ANC Taxiway Centerline Deviations for 747 Aircraft , 2003 .

[8]  Holger Drees,et al.  On Smooth Statistical Tail Functionals , 1998 .

[9]  L. Peng,et al.  Bootstrapping endpoint , 2012, Sankhya A.

[10]  L. Haan,et al.  Residual Life Time at Great Age , 1974 .

[11]  Jan R. Magnus,et al.  Records in Athletics Through Extreme-Value Theory , 2006 .

[12]  B. Gnedenko.  Sur La Distribution Limite Du Terme Maximum D'Une Serie Aleatoire , 1943 .

[13]  A. C. Chiang.  Elements of Dynamic Optimization , 1992 .

[14]  L. Haan,et al.  A moment estimator for the index of an extreme-value distribution , 1989 .

[15]  António B. Pereira,et al.  Detecting finiteness in the right endpoint of light-tailed distributions , 2010 .

[16]  Jan Beirlant,et al.  Generalized Kernel Estimators for the Weibull-Tail Coefficient , 2010 .

[17]  L. Peng,et al.  Bias reduction for endpoint estimation , 2011 .

[18]  Michael Falk,et al.  Some Best Parameter Estimates for Distributions with Finite Endpoint , 1995 .

[19]  Liang Peng,et al.  Does bias reduction with external estimator of second order parameter work for endpoint , 2009 .

[20]  L. Haan,et al.  Bias correction in extreme value statistics with index around zero , 2013 .

[21]  R. Fisher,et al.  Limiting forms of the frequency distribution of the largest or smallest member of a sample , 1928, Mathematical Proceedings of the Cambridge Philosophical Society.

[22]  Laurens de Haan,et al.  How Far Can Man Go , 2013 .