Ciências e Tecnologia | Capítulos/artigos em livros internacionais / Book chapters/papers in international books
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- Population growth and geometrically-thinned extreme value theoryPublication . Brilhante, Maria de Fátima; Gomes, Maria Ivette; Mendonça, Sandra; Pestana, Dinis; Pestana, Pedro Duarte; Henriques-Rodrigues, L.; Menezes, R.; Machado, L.M.; Faria, S.; de Carvalho, M.Starting from the simple Beta(2,2) model, connected to the Verhulst logistic parabola, several extensions are discussed, and connections to extremal models are revealed. Aside from the classical general extreme value model, extreme value models in randomly stopped extremes schemes are also discussed. Logistic and Gompertz growth equations are the usual choice to model sustainable growth. Therefore, observing that the logistic distribution is (geo)max-stable and the Gompertz function is proportional to the Gumbel max-stable distribution, other growth models, related to classical and to geometrically thinned extreme value theory are investigated.
- Risk assessment of vulnerabilities exploitationPublication . Brilhante, Maria de Fátima; Pestana, Pedro Duarte; Rocha, Maria Luísa; Sequeira, Fernando; Henriques-Rodrigues, L.; Menezes, R.; Faria, S.Using the Kolmogorov–Smirnov, Cramér–von Mises and Anderson– Darling tests, and the not so commonly applied Vuong’s test, it is shown that a two components hyperlog-logistic distribution, i.e., a mixture of two geo-max-stable log-logistic distributions, provides a good fit for the time from disclosure to update of vulnerabilities sampled from the CVEdetails.com database. It is also shown that the hyperlog-logistic distribution provides a better fit than a heavy-tailed distribution of maxima, or a log-logistic distribution, or even a heavy-tailed two components hyperexponential distribution. Moreover, ways of incorporating uncertainty and of modeling vulnerabilities lifecycle into the Common Vulnerabilities Scoring System (CVSS), the most widely used score to assess severity of vulnerabilities, are discussed, in order to obtain an improved CVSS calculator and the evolution of a score over time.
