On the estimation of the second order parameter for heavy-tailed distributions

摘要: The extreme-value index is an important parameter in theory since it controls the fi rst order behavior of distribution tail. In literature, numerous estimators this have been proposed especially case heavy-tailed distributions, which situation considered here. Most these depend on k largest observations underlying sample. Their bias controlled by second parameter. to reduce or select best number use, knowledge essential. paper, we propose a simple approach estimate leading both existing and new estimators. We establish general result that can be used easily prove asymptotic normality large literature compare di erent within given family. Some illustrations simulations are also provided.