Everything about Logistic Function 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:
»
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 Function'.
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