Open AccessProbabilistic analysis of linear-quadratic logistic-type models with hybrid uncertainties via probability density functions
Author(s) -
C. Burgos,
Juan Carlos Cortés López,
Elena López-Navarro,
Rafael Villanueva
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2021290
Subject(s) - mathematics , probability density function , random variable , probabilistic logic , quadratic equation , probability distribution , principle of maximum entropy , statistics , geometry
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.