Logistic function

A logistic function or logistic curve is a common S-shaped curve (sigmoid curve) with equation where , the value of the sigmoid's midpoint;, the supremum of the values of the function;, the logistic growth rate or steepness of the curve. For values of in the domain of real numbers from to , the S-curve shown on the right is obtained, with the graph of approaching as approaches and approaching zero as approaches . The standard logistic function, where , is sometimes simply called the sigmoid. It is also sometimes called the expit, being the inverse of the logit.

Caption: enInverted S-curve model for crop yield versus soil salinity.; enS-curve model for crop yield versus depth of water table.
Comment: enA logistic function or logistic curve is a common S-shaped curve (sigmoid curve) with equation where , the value of the sigmoid's midpoint;, the supremum of the values of the function;, the logistic growth rate or steepness of the curve. For values of in the domain of real numbers from to , the S-curve shown on the right is obtained, with the graph of approaching as approaches and approaching zero as approaches . The standard logistic function, where , is sometimes simply called the sigmoid. It is also sometimes called the expit, being the inverse of the logit.
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Has abstract: enA logistic function or logistic curve is a common S-shaped curve (sigmoid curve) with equation where , the value of the sigmoid's midpoint;, the supremum of the values of the function;, the logistic growth rate or steepness of the curve. For values of in the domain of real numbers from to , the S-curve shown on the right is obtained, with the graph of approaching as approaches and approaching zero as approaches . The logistic function finds applications in a range of fields, including biology (especially ecology), biomathematics, chemistry, demography, economics, geoscience, mathematical psychology, probability, sociology, political science, linguistics, statistics, and artificial neural networks. A generalization of the logistic function is the hyperbolastic function of type I. The standard logistic function, where , is sometimes simply called the sigmoid. It is also sometimes called the expit, being the inverse of the logit.
Image: enBarley S-curve.png; enSugarcane S-curve.png
Is primary topic of: Logistic function
Label: enLogistic function
Link from a Wikipage to an external page: papers.tinbergen.nl/02119.pdf; www.sciencedaily.com/releases/2011/07/110720151541.htm; books.google.com/books%3Fid=Ac5bgYVk8kwC; books.google.com/books%3Fid=zYAcGbp17nYC; jeffreyfreeman.me/restricted-logarithmic-growth-with-injection/; web.archive.org/web/20060914155939/http:/luna.cas.usf.edu/~mbrannic/files/regression/Logistic.html; jsxgraph.uni-bayreuth.de/wiki/index.php/Logistic_process; rasch.org/rmt/rmt64k.htm; www.sciencecodex.com/seeing_the_scurve_in_everything
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SameAs: 8LHy; Equassion logìstica; Equazione logistica; Fonction logistique (Verhulst); Função logística; Funció logística; Función logística; Funtzio logistiko; Hàm logistic; Logistic function; Logistic functions; Logistická funkce; Logistická funkcia; Logistinen funktio; Logistische functie; Logistische Funktion; Logistisk funktion; Logistisk funktion; Logistisk vekst; Lojistik fonksiyon; m.0lj5d; Mezinbûna lojistîkî; Q1052379; Логистическое уравнение; Логістична рівність; פונקציה לוגיסטית; تابع لجستیک; دالة لوجستية; 逻辑斯谛函数; 로지스틱 함수
SeeAlso: Gompertz curve
Subject: Category:Differential equations; Category:Growth curves; Category:Logistic regression; Category:Population; Category:Population ecology; Category:Special functions
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Title: enLogistic Equation; enSigmoid Function
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