 A parametric alternative to the Hill estimator for heavy-tailed distributionsJoseph H.T. Kim and Joocheol Kim Journal of Banking & Finance, 2015, vol. 54, issue C, 60-71 Abstract: Despite its wide use, the Hill estimator and its plot remain to be difficult to use in Extreme Value Theory (EVT) due to substantial sampling variations in extreme sample quantiles. In this paper, we propose a new plot we call the eigenvalue plot which can be seen as a generalization of the Hill plot. The theory behind the plot is based on a heavy-tailed parametric distribution class called the scaled Log phase-type (LogPH) distributions, a generalization of the ordinary LogPH distribution class which was previously used to model insurance claims data. We show that its tail property and moment condition are well aligned with EVT. Based on our findings, we construct the eigenvalue plot from fitting a shifted PH distribution to the excess log data with a minimal phase size. Through various numerical examples we illustrate and compare our method against the Hill plot. Keywords: Hill estimator; Tail index; Extreme value theory; Generalized Pareto distribution; Scaled Log phase-type distribution (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:jbfina:v:54:y:2015:i:c:p:60-71 DOI: 10.1016/j.jbankfin.2014.12.020 Access Statistics for this article Journal of Banking & Finance is currently edited by Ike Mathur More articles in Journal of Banking & Finance from Elsevier |
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