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A logistic function or logistic curve is a common S-shaped curve ( sigmoid curve) with the equation. where. , the value of the function's midpoint; , the supremum of the values of the function; , the logistic growth rate or steepness of the curve. [1] Standard logistic function where. For values of in the domain of real numbers from to , the S ...
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.
Logistic function, solution of the logistic map's continuous counterpart: the Logistic differential equation. Lyapunov stability#Definition for discrete-time systems; Malthusian growth model; Periodic points of complex quadratic mappings, of which the logistic map is a special case confined to the real line
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 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 ...
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 tails (higher kurtosis ).
Under the logistic model, population growth rate between these two limits is most often assumed to be sigmoidal (Figure 1). There is scientific evidence that some populations do grow in a logistic fashion towards a stable equilibrium – a commonly cited example is the logistic growth of yeast. The equation describing logistic growth is:
Gompertz function. The Gompertz curve or Gompertz function is a type of mathematical model for a time series, named after Benjamin Gompertz (1779–1865). It is a sigmoid function which describes growth as being slowest at the start and end of a given time period. The right-side or future value asymptote of the function is approached much more ...