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Logistic function. A logistic function or logistic curve is a common S-shaped curve (sigmoid curve) with the equation. where. is the carrying capacity, the supremum of the values of the function; is the logistic growth rate, the steepness of the curve; and. is the value of the function's midpoint.
Hubbert linearization. The Hubbert linearization is a way to plot production data to estimate two important parameters of a Hubbert curve, the approximated production rate of a nonrenewable resource following a logistic distribution: the logistic growth rate and. the quantity of the resource that will be ultimately recovered.
The von Bertalanffy growth function (VBGF), or von Bertalanffy curve, is a type of growth curve for a time series and is named after Ludwig von Bertalanffy. It is a special case of the generalised logistic function. The growth curve is used to model mean length from age in animals. [ 1 ] The function is commonly applied in ecology to model fish ...
A sigmoid function is any mathematical function whose graph has a characteristic S-shaped or sigmoid curve. A common example of a sigmoid function is the logistic function shown in the first figure and defined by the formula: [1] Other standard sigmoid functions are given in the Examples section. In some fields, most notably in the context of ...
The generalized logistic function or curve is an extension of the logistic or sigmoid functions. Originally developed for growth modelling, it allows for more flexible S-shaped curves. The function is sometimes named Richards's curve after F. J. Richards, who proposed the general form for the family of models in 1959.
The Hubbert curve is an approximation of the production rate of a resource over time. It is a symmetric logistic distribution curve, [1] often confused with the "normal" gaussian function. It first appeared in "Nuclear Energy and the Fossil Fuels," geologist M. King Hubbert 's 1956 presentation to the American Petroleum Institute, as an ...
where is the binary entropy function [1] In probability theory and statistics, the logistic distribution is a continuous probability distribution. Its cumulative distribution function is the logistic function, which appears in logistic regression and feedforward neural networks. It resembles the normal distribution in shape but has heavier ...
Logistic growth never is negative, but in the saturation area, the growth is as small as before the market took off. (In the example all curves are scaled to cover the range between 0 and 1.) In economics, market saturation is a situation in which a product has become diffused (distributed) within a market; [1] the actual level of saturation ...