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

We provide a full stochastic description, via the first probability density function, of solution linear-quadratic logistic-type differential equation whose parameters involve both continuous and discrete random variables with arbitrary distributions. For sake generality, initial condition is assumed to be variable too. use Dirac delta function unify treatment hybrid (discrete-continuous) uncertainty. Under general hypotheses, we also compute time until certain value (usually representing population) logistic model reached. The theoretical results are illustrated by means several examples, including an application modelling number users Spotify using real data. apply Principle Maximum Entropy assign plausible distributions parameters.