CHAPTER 2 Tail Index Estimation of Heavy-tailed Distributions 2 . 1

Content Provider	Semantic Scholar
Copyright Year	2014
Abstract	In many diverse fields such as meteriology, finance, hydrology, climatology, environmental sciences, telecommunication, insurance and genetics, heavy-tailed distributions are recommended to model the data, see Embrechts et al. (1997) and hence the problem of estimation of the tail index of a heavy-tailed distribution has been paid much attention in recent years. The tail shape of heavy-tailed distributions resembles to a first approximation the hyperbolic shape of the Pareto distribution characterized by the so-called tail index. Besides, this parameter plays a key role in connection with determination of extreme quantiles, upper tail probabilities, mean excess functions and excess of loss and stop reinsurance premium etc. Small relative errors in the estimation of tail index can produce large relative errors in estimation of such quantities. Moreover, in the context of semi-parametric
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