Title: Population growth, Extreme Value Theory (EVT) and geometrically thinned EVT Authors:  Ivette Gomes - FCiencias.ID, Universidade de Lisboa and CEAUL (Portugal) [presenting]
Abstract: Order statistics and products of powers of independent uniform random variables originate families of random variables, such as Beta and Logarithmic random variables, with natural parameters, which can be further generalised using fractional parameters. The probability density function of the middle-order statistic of three independent uniform random variables is proportional to the logistic parabola, leading to the logistic population growth model via the Verhulst differential equation. Extensions of the Verhulst model, connected to Beta and Logarithmic densities, lead to population growth models equilibrium such as the Gompertz model, tied to the Gumbel extreme value model, a max-stable model of high relevance in extreme value theory. Logistic and Gompertz growth equations are the usual choices to model sustainable growth. Observing that the logistic distribution is max-geo-stable and the Gompertz function is proportional to the Gumbel max-stable distribution, other growth models related to geometrically thinned EVT are investigated.