Isabel Fraga Alves

Estimation of the finite right endpoint in the Gumbel domain

A simple estimator for the finite right endpoint of a distribution function in the Gumbel max-domain of attraction is proposed. Large sample properties such as consistency and the asymptotic distribution are derived. A simulation study is presented.

Ratio of Maximum to the Sum for Testing Super Heavy Tails

An extreme value approach to the modeling of rare and damaging events quite frequently involves heavy tailed distributions associated with power decaying tails. The positive counterpart of this power, which determines the tail heaviness of the distribution function pertaining to the sample observations, is consensually known as the tail index. In this paper, we allow the tail index

How Far Can Man Go

α

A general estimator for the right endpoint with an application to supercentenarian women’s records

to be zero so as to embrace the class of super-heavy tailed distributions. We then present a test statistic consisting of the ratio of maximum to the sum of log-excesses in order to discern between distributions with heavy and super-heavy tails. Under suitable yet reasonable assumptions, we cast an account of consistency of the Hill estimator for α equal to zero from the asymptotic features of the referred testing procedure.

Fitting tails affected by truncation

In this chapter we address the question of “What is the Largest Jump at Man’s reach, given today’s state of the art?” To answer that question it will be used the best from the best, i.e., the data will be collected from the best “jumpers” from World Athletics Competitions—“Long Jump Men Outdoors” event. Our approach to the problem is based on the probability theory of extreme values (EVT) and the corresponding statistical techniques. We shall only use the top performances of World top lists. Our estimated ultimate record, i.e., the right endpoint of the jumping event, tells us what is possible to infer about the possible personal best mark, given today’s knowledge, sports conditions and rules.

Parametric and Semi-parametric Approaches to Extreme Rainfall Modelling

We extend the setting of the right endpoint estimator introduced in Fraga Alves and Neves (Statist. Sinica 24, 1811–1835, 2014) to the broader class of light-tailed distributions with finite endpoint, belonging to some domain of attraction induced by the extreme value theorem. This stretch enables a general estimator for the finite endpoint, which does not require estimation of the (supposedly non-positive) extreme value index. A new testing procedure for selecting max-domains of attraction also arises in connection with the asymptotic properties of the general endpoint estimator. The simulation study conveys that the general endpoint estimator is a valuable complement to the most usual endpoint estimators, particularly when the true extreme value index stays above −1/2, embracing the most common cases in practical applications. An illustration is provided via an extreme value analysis of supercentenarian women data.

High quantiles estimation with Quasi-PORT and DPOT: An application to value-at-risk for financial variables

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 et al. (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

A test procedure for detecting super-heavy tails

\xi>-1/2

Tail fitting for truncated and non-truncated Pareto-type distributions

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.

EFFE-Escreves como falas – falas como escreves?

In a meteorological setup, considering a data set of daily rainfall in Barcelos, Portugal, a survey of possible parametric and semi-parametric approaches in Extreme Value Theory is presented, with the main goal of the analyzing high observations of records over time, since these might entail negative consequences for society. These analysis embraces estimation of several extreme value parameters, including return levels associated with \(T\)-year return periods, for large \(T\).