Modeling Risk of Extreme Events in Generalized Verhulst Models

Abstract

A very popular model in population dynamics, which has been around since the first half of the nineteenth century, is the Verhulst logistic model. However, some limitations of this model have provided grounds to propose more sophisticated growth models using, for instance, the former as a basis. Since the Verhulst model and some generalizations of it are closely connected to extreme value distributions, either max-geometric-stable or max-stable, we show that the parameter attached to the retroaction factor of these generalized models establishes, on its own, which extreme value distribution is adequate to model risks of extreme events in population dynamics.

Keywords

• Extreme value distributions
• generalized Verhulst models
• growth and retroaction parameters
• max-geometric-stable distributions
• population dynamics