Three different ways (compounding, beta transform, and order statistics) to derive a reparametrized form (g-log) of the Verhulst generalized logistic growth curve, are taken to characterize this g-log and thus its life-time transforms, especially some generating function and hazard rate properties (recursive, MIFR, asymptotically constant).
Two limiting forms of the g-log are derived demonstrating the close relation to standard life-time models: the exponential and the extreme- value distribution. Relations to other standard probability models are shown.