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Logit Transformation

\begin{figure}\begin{center}\BoxedEPSF{LogitTransform.epsf scaled 700}\end{center}\end{figure}

The function

z=f(x)=\ln\left({x\over 1-x}\right).

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

f''(x)={2x-1\over x^2(x-1)^2}=0.

Applying the logit transformation to values obtained by iterating the Logistic Equation generates a sequence of Random Numbers having distribution

P_z={1\over \pi(e^{x/2}+e^{-x/2})},

which is very close to a Gaussian Distribution.


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.

© 1996-9 Eric W. Weisstein