Sigmoidsi

Sigmoidsi is a term used in mathematical modeling to refer to a family of sigmoidal, S-shaped growth curves that describe processes transitioning from a lower bound to an upper bound. The term signals a category rather than a single equation, encompassing several well-known models that capture saturation effects in real-world data.

The sigmoidsi family is not a single equation but a category that includes standard models such as the logistic function, the Gompertz function, and the Richards curve. Common features of sigmoidsi curves include an S-shaped trajectory, a lower asymptote, an upper asymptote, and a finite growth period governed by rate and location parameters that shape the timing and steepness of the transition from slow to rapid growth.

Representative forms often cited within the sigmoidsi umbrella include:

- Logistic: y = L / (1 + e^{-k(x - x0)})

- Gompertz: y = L · exp(-b e^{-k x})

- Richards: y = L / [1 + a e^{-k x}]^{1/m}

Here L denotes the upper asymptote, and k, x0, b, a, and m are shape parameters that modulate lag, growth rate, and saturation.

Applications of sigmoidsi models appear in population biology, epidemiology, pharmacology, environmental science, and technology diffusion, where processes start slowly, accelerate, and then saturate. In formal literature, sigmoidsi is not a standard term, but the underlying models are widely used under the established names of logistic, Gompertz, and Richards curves. See also logistic function, Gompertz function, Richards curve, and sigmoidal growth.