Gompertz Substitution Forecasting

Both are S-shaped curves bounded by a ceiling, but they differ in symmetry. The logistic is symmetric about its midpoint, so its fastest growth occurs when adoption reaches half the ceiling. The Gompertz curve is asymmetric: its inflection point falls early, at about 37 percent of the ceiling, so it accelerates quickly and then approaches saturation slowly along a long tail. Choosing between them is a substantive judgment about the diffusion mechanism, and analysts often fit both and compare residuals to see which better matches the historical pattern before extrapolating.

The ceiling L anchors the entire forecast. Because the curve is defined relative to L, every projected adoption level and every threshold-crossing date depends on where the ceiling is placed. A ceiling set too high stretches the timeline and understates how mature the technology already is, while one set too low compresses it. Glenn and Gordon stress bounding L with external evidence — market size, physical limits, or the share the technology can plausibly serve — rather than letting an unconstrained fit choose it, since an ill-determined ceiling is the dominant source of error in growth-curve forecasting.

Enough to have observed, or to be near, the inflection where growth is fastest. In the slow early phase many different S-curves pass through the same handful of points, so the data cannot yet distinguish a Gompertz path from a logistic or a faster-saturating one, and extrapolations are unreliable. Confidence improves markedly once the series brackets the steep middle portion of the curve. Until then, the prudent practice is to treat the projection as provisional, report wide sensitivity bands, and corroborate it with expert judgment rather than relying on the fit alone.