Logistic function Totally Explained

Everything about Logistic Curve totally explained

A logistic function or logistic curve models the S-curve of growth of some set P. The initial stage of growth is approximately exponential; then, as saturation begins, the growth slows, and at maturity, growth stops.
A logistic function is defined by the mathematical formula:
ť

P(t;a,m,n,	au) = afrac!

with boundary condition P(0) = 1/2. Equation (2) is the continuous version of the logistic map.
The sigmoid curve shows early exponential growth for negative t, which slows to linear growth of slope 1/4 near t = 0, then approaches y = 1 with an exponentially decaying gap.
The logistic function is the inverse of the natural logit function and so can be used to convert the logarithm of odds into a probability; the conversion from the log-likelihood ratio of two alternatives also takes the form of a sigmoid curve.

History

The Verhulst equation, (1), was first published by Pierre F. Verhulst in 1838 after he'd read Thomas Malthus' An Essay on the Principle of Population.
Verhulst derived his logistic equation to describe the self-limiting growth of a biological population. The equation is also sometimes called the Verhulst-Pearl equation following its rediscovery in 1920. Alfred J. Lotka derived the equation again in 1925, calling it the law of population growth.

Further Information

Get more info on 'Logistic Curve'.

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