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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.
A sigmoid function is any mathematical function whose graph has a characteristic S-shaped curve 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 ...
The logistic growth curve depicts how population growth rate and carrying capacity are inter-connected. As illustrated in the logistic growth curve model, when the population size is small, the population increases exponentially. However, as population size nears carrying capacity, the growth decreases and reaches zero at K.
1) where x n is a number between zero and one, which represents the ratio of existing population to the maximum possible population. This nonlinear difference equation is intended to capture two effects: reproduction , where the population will increase at a rate proportional to the current population when the population size is small, starvation (density-dependent mortality), where the growth ...
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 ).
The Hubbert peak theory says that for any given geographical area, from an individual oil-producing region to the planet as a whole, the rate of petroleum production tends to follow a bell-shaped curve. It is one of the primary theories on peak oil . Choosing a particular curve determines a point of maximum production based on discovery rates ...
A Malthusian growth model, sometimes called a simple exponential growth model, is essentially exponential growth based on the idea of the function being proportional to the speed to which the function grows. The model is named after Thomas Robert Malthus, who wrote An Essay on the Principle of Population (1798), one of the earliest and most ...