16 documents found, page 1 of 2
Book of Abstracts of SPE 2021
Alpiza-Jara, Russell; Gomes, Dulce; Henriques-Rodrigues, Lígia; Filipe, Patricia A.Book of Abstracts of SPE 2021
Estimation of the Weibull tail coefficient through the power-mean-of-order p
Caeiro, Frederico; Gomes, Maria Ivette; Henriques-Rodrigues, LígiaThe Weibull tail coefficient (WTC) is the parameter θ θ in a right-tail function of the type F¯:=1−F F¯:=1−F, such that H:=−ln F¯ is a regularly varying function at infinity with an index of regular variation equal to θ∈R+. In a context of extreme value theory for maxima, it is possible to prove that we have an extreme value index (EVI) ξ=0, but usually a very slow rate of convergence. Most of the recent WTC-es...
A Generalized Mean Under a Non-Regular Framework and Extreme Value Index Estima...
Gomes, Maria Ivette; Henriques-Rodrigues, Lígia; Pestana, DinisThe Hill estimator, one of the most popular extreme value index (EVI) estimators under a heavy right-tail framework, i.e. for a positive EVI, here denoted by ξ, is an average of the log-excesses. Consequently, it can be regarded as the logarithm of the geometric mean or mean of order p = 0 of an adequate set of systematic statistics. We can thus more generally consider any real p, the mean of order p (MOp) of t...
A Generalized Mean Under a Non-Regular Framework and Extreme Value Index Estima...
Gomes, Maria Ivette; Henriques-Rodrigues, Lígia; Pestana, DinisThe Hill estimator, one of the most popular extreme value index (EVI) estimators under a heavy right-tail framework, i.e. for a positive EVI, here denoted by ξ, is an average of the log-excesses. Consequently, it can be regarded as the logarithm of the geometric mean or mean of order p = 0 of an adequate set of systematic statistics. We can thus more generally consider any real p, the mean of order p (MOp) of t...
Estimação de um índice de valores extremos positivo através de médias generaliz...
Gomes, Maria Ivette; Henriques-Rodrigues, Lígia; Pestana, DinisO estimador de Hill é o estimador mais popular de um índice de valores extremos (EVI, do inglês ‘extreme value index’) positivo, denotado por ξ. Trata-se de uma média aritmética, sendo consequentemente o logaritmo da média geométrica, i.e. da média- de-ordem-0, de estatísticas adequadas, função das estatísticas ordinais de topo associadas a uma amostra aleatória. Podemos mais geralmente considerar a média-de-or...
Recent Developments in Statistics and Data Science
Bispo, Regina; Henriques-Rodrigues, Lígia; Alpizar-Jara, Russell; de Carvalho, MiguelDescribes new developments in statistics and data science with applications Provides motivational and interdisciplinary work for graduate students and researchers Comprises selected contributions presented to the Congress of the Portuguese Statistical Society.
Minimum-variance reduced-bias estimation of the extreme value index: A theoreti...
Caeiro, Frederico; Henriques-Rodrigues, Lígia; Gomes, M. Ivette; Cabral, IvanildaIn extreme value (EV) analysis, the EV index (EVI), , is the primary parame- ter of extreme events. In this work, we consider positive, that is, we assume that F is heavy tailed. Classical tail parameters estimators, such as the Hill, the Moments, or the Weissman estimators, are usually asymptotically biased. Con- sequently, those estimators are quite sensitive to the number of upper order statistics used in th...
Non-regular Frameworks and the Mean-of-Order p Extreme Value Index Estimation
Gomes, M. Ivette; Henriques-Rodrigues, Lígia; Pestana, DinisMost of the estimators of parameters of rare and large events, among which we dis- tinguish the extreme value index (EVI) for maxima, one of the primary parameters in statistical extreme value theory, are averages of statistics, based on the k upper observations. They can thus be regarded as the logarithm of the geometric mean, i.e. the logarithm of the power mean of order p = 0 of a certain set of statistics. ...
Box-Cox Transformations and Bias Reduction in Extreme Value Theory
Henriques-Rodrigues, Lígia; Gomes, M. IvetteThe Box-Cox transformations are used to make the data more suitable for statistical analysis. We know from the literature that this transformation of the data can increase the rate of convergence of the tail of the distribution to the generalized extreme value distribution, and as a byproduct, the bias of the estimation procedure is reduced. The reduction of bias of the Hill estimator has been widely addressed ...
The Use of Generalized Means in the Estimation of the Weibull Tail Coefficient
Caeiro, Frederico; Henriques-Rodrigues, Lígia; Gomes, M. IvetteDue to the specificity of the Weibull tail coefficient, most of the estimators available in the literature are based on the log excesses and are consequently quite similar to the estimators used for the estimation of a positive extreme value index. The interesting performance of estimators based on generalized means leads us to base the estimation of the Weibull tail coefficient on the power mean-of-order-. Con...