Probabilistic analysis of linear-quadratic logistic-type models with hybrid uncertainties via probability density functions
| Autor: | Elena López-Navarro, Clara Burgos, Rafael Jacinto Villanueva, Juan Carlos Cortés |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Random variable transformation method
hybrid uncertainty Differential equation uncertainty quantification General Mathematics Population Dirac delta function Probability density function Random linear-quadratic logistic differential equation symbols.namesake first probability density function Applied mathematics Initial value problem Principle Maximum Entropy Uncertainty quantification education random linear-quadratic logistic differential equation Mathematics education.field_of_study Hybrid uncertainty Principle of maximum entropy lcsh:Mathematics random variable transformation method lcsh:QA1-939 symbols First probability density function MATEMATICA APLICADA Random variable principle maximum entropy |
| Zdroj: | AIMS Mathematics, Vol 6, Iss 5, Pp 4938-4957 (2021) RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia instname |
| ISSN: | 2473-6988 |
| DOI: | 10.3934/math.2021290?viewType=HTML |
| Popis: | [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 This work has been supported by the Spanish Ministerio de Economa, Industria y Competitividad (MINECO) , the Agencia Estatal de Investigaci on (AEI) and Fondo Europeo de Desarrollo Regional (FEDER UE) grant MTM201789664P. Computations have been carried thanks to the collaboration of Raul San Julian Garces and Elena Lopez Navarro granted by European Union through the Operational Program of the European Regional Development Fund (ERDF) /European Social Fund (ESF) of the Valencian Community 2014-2020, grants GJIDI/2018/A/009 and GJIDI/2018/A/010, respectively |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|