From the wikipedia article on the Gompertz function: "The right-hand or future value asymptote of the function is approached much more gradually by the curve than the left-hand or lower valued asymptote."
Is there a sigmoidal, asymmetrical function, similar to the Gompertz, so that the behaviour at the asymptotes are reversed, that is: The right-hand or future value asymptote of the function is approached much more rapidly by the curve than the left-hand or lower valued asymptote.