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Logit Transformation

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LogitTransformation

The function

z=f(x)=ln(x/(1-x)).
(1)

This function has an inflection point at x=1/2, where

f^('')(x)=(2x-1)/(x^2(x-1)^2)=0.
(2)

Applying the logit transformation to values obtained by iterating the logistic equation generates a sequence of random numbers having distribution

P_z=1/(pi(e^(x/2)+e^(-x/2))),
(3)

which is very close to a normal distribution.

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References

Collins, J.; Mancilulli, M.; Hohlfeld, R.; Finch, D.; Sandri, G.; and Shtatland, E. "A Random Number Generator Based on the Logit Transform of the Logistic Variable." Computers in Physics 6, 630-632, 1992.Pickover, C. A. Keys to Infinity. New York: Wiley, pp. 244-245, 1995.

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Logit Transformation

Cite this as:

Weisstein, Eric W. "Logit Transformation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LogitTransformation.html

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