A contribution to the estimation of the tail index of heavy -tailed distributions.

The problem of estimating the tail index in heavy-tailed distributions is very important in a variety of applications. Three new graphical methods, the H(k ) plot, the K(k ) plot, and the Sum plot, are proposed for choosing the appropriate number of upper order statistics used in the estimation of the tail index. The Sum plot exhibits stable patterns and facilitates the choice of the correct number of upper order statistics involved in this estimation. Its theoretical properties are investigated. The performance of these procedures in finite samples are examined through a simulation study when the data are from a Pareto, an Inverted Gamma, and a Symmetric alpha-Stable distribution and are also applied to several real data sets. The results suggest that the Sum plot, together with the Hill estimator, overcomes many of the uncertainties present in some of the most common techniques used in the estimation of the tail index, such as the Hill, the Zipf, and the CD plots.Ph.D.Pure SciencesStatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/132932/2/3058046.pd