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logisticfunction

logistic function

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There are 16 letters in LOGISTICFUNCTION ( C³F⁴G²I¹L¹N¹O¹S¹T¹U¹ )

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Definitions of logistic function in various dictionaries:

LOGISTIC FUNCTION - A logistic function or logistic curve is a common "S" shape (sigmoid curve), with equation: f ( x ) ...

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Logistic function description
A logistic function or logistic curve is a common "S" shape (sigmoid curve), with equation:* * * * f * ( * x * ) * = * * * L * * 1 * + * * e * * − * k * ( * x * − * * x * * 0 * * * ) * * * * * * * * {\displaystyle f(x)={\frac {L}{1+e^{-k(x-x_{0})}}}} * where * * e = the natural logarithm base (also known as Euler's number), * x0 = the x-value of the sigmoid's midpoint, * L = the curve's maximum value, and * k = the logistic growth rate or steepness of the curve.For values of x in the domain of real numbers from −∞ to +∞, the S-curve shown on the right is obtained, with the graph of f approaching L as x approaches +∞ and approaching zero as x approaches −∞. * The function was named in 1844 (published 1845) by Pierre François Verhulst, who studied it in relation to population growth. The initial stage of growth is approximately exponential (geometric); then, as saturation begins, the growth slows to linear (arithmetic), and at maturity, growth stops. Verhulst did not explain the choice of the term "logistic" (French: logistique), but it follows his discussion of arithmetic growth and geometric growth (whose curve he calls a logarithmic curve, instead of the modern term exponential curve), and thus "logistic growth" is presumably named by analogy with arithmetic and geometric, logistic being from Ancient Greek: λογῐστῐκός, translit. logistikós, a traditional division of Greek mathematics, and in contrast to the logarithmic curve. The term is unrelated to the military and management term logistics, which is instead from French: logis "lodgings", though some believe the Greek term also influenced logistics; see Logistics § Origin for details. * The logistic function finds applications in a range of fields, including artificial neural networks, biology (especially ecology), biomathematics, chemistry, demography, economics, geoscience, mathematical psychology, probability, sociology, political science, linguistics, and statistics.

Logistic function description

A logistic function or logistic curve is a common "S" shape (sigmoid curve), with equation:*
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* {\displaystyle f(x)={\frac {L}{1+e^{-k(x-x_{0})}}}}
* where
*
* e = the natural logarithm base (also known as Euler's number),
* x0 = the x-value of the sigmoid's midpoint,
* L = the curve's maximum value, and
* k = the logistic growth rate or steepness of the curve.For values of x in the domain of real numbers from −∞ to +∞, the S-curve shown on the right is obtained, with the graph of f approaching L as x approaches +∞ and approaching zero as x approaches −∞.
* The function was named in 1844 (published 1845) by Pierre François Verhulst, who studied it in relation to population growth. The initial stage of growth is approximately exponential (geometric); then, as saturation begins, the growth slows to linear (arithmetic), and at maturity, growth stops. Verhulst did not explain the choice of the term "logistic" (French: logistique), but it follows his discussion of arithmetic growth and geometric growth (whose curve he calls a logarithmic curve, instead of the modern term exponential curve), and thus "logistic growth" is presumably named by analogy with arithmetic and geometric, logistic being from Ancient Greek: λογῐστῐκός, translit. logistikós, a traditional division of Greek mathematics, and in contrast to the logarithmic curve. The term is unrelated to the military and management term logistics, which is instead from French: logis "lodgings", though some believe the Greek term also influenced logistics; see Logistics § Origin for details.
* The logistic function finds applications in a range of fields, including artificial neural networks, biology (especially ecology), biomathematics, chemistry, demography, economics, geoscience, mathematical psychology, probability, sociology, political science, linguistics, and statistics.

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