Generalized Beta Models and Population Growth: So Many Routes to Chaos

Logistic and Gompertz growth equations are the usual choice to model sustainable immoderate causing depletion of resources, respectively. Observing that logistic distribution is geo-max-stable function proportional Gumbel max-stable distribution, we investigate other models either distributions (log-logistic backward log-logistic) or (Fréchet max-Weibull). We show former arise when in hyper-logistic Blumberg equation, connected Beta (p,q) function, use fractional exponents p−1=1∓1/α q−1=1±1/α, latter hyper-Gompertz-Turner logarithmic factor real eventually fractional. The a BetaBoop establishes interesting connections Probability Theory, Riemann–Liouville’s integrals, higher-order monotonicity convexity generalized unimodality, map paradigm inspires investigation dynamics hyper-Gompertz maps.