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Fitting tails affected by truncation

Tijdschriftbijdrage - Tijdschriftartikel

© 2017, Institute of Mathematical Statistics. All rights reserved. In several applications, ultimately at the largest data, truncation effects can be observed when analysing tail characteristics of statistical distributions. In some cases truncation effects are forecasted through physical models such as the Gutenberg-Richter relation in geophysics, while at other instances the nature of the measurement process itself may cause under recovery of large values, for instance due to flooding in river discharge readings. Recently, Beirlant, Fraga Alves and Gomes (2016) discussed tail fitting for truncated Pareto-type distributions. Using examples from earthquake analysis, hydrology and diamond valuation we demonstrate the need for a unified treatment of extreme value analysis for truncated heavy and light tails. We generalise the classical Peaks over Threshold approach for the different max-domains of attraction with shape parameter ξ > −1/2 to allow for truncation effects. We use a pseudo maximum likelihood approach to estimate the model parameters and consider extreme quantile estimation and reconstruction of quantile levels before truncation whenever appropriate. We report on some simulation experiments and provide some basic asymptotic results.
Tijdschrift: Electronic Journal of Statistics
ISSN: 1935-7524
Issue: 1
Volume: 11
Pagina's: 2026 - 2065
Jaar van publicatie:2017
BOF-keylabel:ja
IOF-keylabel:ja
BOF-publication weight:1
CSS-citation score:1
Auteurs:International
Authors from:Higher Education
Toegankelijkheid:Open