| Autor: |
Clara Burgos, Juan Carlos Cortés, Elena López-Navarro, Rafael Jacinto Villanueva |
| Jazyk: |
angličtina |
| Rok vydání: |
2021 |
| Předmět: |
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| Zdroj: |
AIMS Mathematics, Vol 6, Iss 5, Pp 4938-4957 (2021) |
| Druh dokumentu: |
article |
| ISSN: |
2473-6988 |
| DOI: |
10.3934/math.2021290?viewType=HTML |
| Popis: |
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. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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