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Ciências e Tecnologia / Sciences and Technology

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http://hdl.handle.net/10400.2/1041

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Percorrer Ciências e Tecnologia / Sciences and Technology por Domínios Científicos e Tecnológicos (FOS) "Ciências Naturais::Matemáticas"

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  • Generalized beta models and population growth: so many routes to chaos
    Publication . Brilhante, Maria de Fátima; Gomes, Maria Ivette; Mendonça, Sandra; Pestana, Dinis; Pestana, Pedro Duarte
    Logistic and Gompertz growth equations are the usual choice to model sustainable growth and immoderate growth causing depletion of resources, respectively. Observing that the logistic distribution is geo-max-stable and the Gompertz function is proportional to the Gumbel max-stable distribution, we investigate other models proportional to either geo-max-stable distributions (log- logistic and backward log-logistic) or to other max-stable distributions (Fréchet or max-Weibull). We show that the former arise when in the hyper-logistic Blumberg equation, connected to the Beta (p, q) function, we use fractional exponents p − 1 = 1 ∓ 1/α and q − 1 = 1 ± 1/α, and the latter when in the hyper-Gompertz-Turner equation, the exponents of the logarithmic factor are real and eventually fractional. The use of a BetaBoop function establishes interesting connections to Probability Theory, Riemann–Liouville’s fractional integrals, higher-order monotonicity and convexity and generalized unimodality, and the logistic map paradigm inspires the investigation of the dynamics of the hyper- logistic and hyper-Gompertz maps.
    2023-01Artigo científico Acesso aberto Ver mais
  • Population growth and geometrically-thinned extreme value theory
    Publication . 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.
    2025Capítulo de livro Acesso restrito Ver mais