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Estimation Of Tail Indices Of Heavy-Tailed Distributions
Mathematics and Statistics
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Heavy-tailed distributions have found many real life applications in analyzingextreme values. Therefore extreme value theory has received much attentionin recent years. Several estimators for the tail index of heavy-tailed distributionshave been proposed in the literature and their properties have been established.These estimators suffer from some drawbacks. Most of the estimatorsincluding Hill and Pickands, make use of intermediate upper order statistics,X(k(n)), X(k(n)+1), ......, X(n). Choosing the suitable value of k is painstaking work.The estimated values can be highly sensitive to the choice of k and the choice ofslowly varying function. Here, a simple and very useful estimator is proposed andits operating characteristics are examined in terms of its bias and mean-squared errorproperties. To compare with other estimators, we introduce several slowlyvarying functions and generate some synthetic data. Then we compute our newestimator using the generated data and compare with other estimators. In addition,using the new estimator we develop some block estimators and examine the behaviorof these block estimators too. These block estimators show excellent results forevery survival function. The estimators are illustrated on real data-sets.