Probabilistic analysis of linear-quadratic logistic-type models with hybrid uncertainties via probability density functions

[EN] We provide a full stochastic description, via the first probability density function, of the solution of linear-quadratic logistic-type differential equation whose parameters involve both continuous and discrete random variables with arbitrary distributions. For the sake of generality, the init...

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Detalles Bibliográficos
Autores: Burgos-Simon, Clara|||0000-0001-6385-4263, Cortés, J.-C.|||0000-0002-6528-2155, López-Navarro, Elena|||0000-0003-0164-9007, Villanueva Micó, Rafael Jacinto|||0000-0002-0131-0532
Tipo de recurso: artículo
Fecha de publicación:2021
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/180500
Acceso en línea:https://riunet.upv.es/handle/10251/180500
Access Level:acceso abierto
Palabra clave:Hybrid uncertainty
Random linear-quadratic logistic differential equation
First probability density function
Random variable transformation method
Uncertainty quantification
Principle Maximum Entropy
MATEMATICA APLICADA
Descripción
Sumario:[EN] We provide a full stochastic description, via the first probability density function, of the solution of linear-quadratic logistic-type differential equation whose parameters involve both continuous and discrete random variables with arbitrary distributions. For the sake of generality, the initial condition is assumed to be a random variable too. We use the Dirac delta function to unify the treatment of hybrid (discrete-continuous) uncertainty. Under general hypotheses, we also compute the density of time until a certain value (usually representing the population) of the linear-quadratic logistic model is reached. The theoretical results are illustrated by means of several examples, including an application to modelling the number of users of Spotify using real data. We apply the Principle Maximum Entropy to assign plausible distributions to model parameters