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Limit of mean of Iterations of f(x)=(ln(x);x>0,ln(-x) x<0) =-Omega constant for all x
#9
If we analyize the distribution of Average over 100 points per Iteration (over 5000 iterations) , then distribution in both cases ln(mod(x) and ln(mod(1/x)) is 3-parameter LogNormal with parameters:


Scale parametes ,

Shape parameter ,

location parameter

[url] http://en.wikipedia.org/wiki/Log-normal_distribution[/url]

While if we analyze distribution of Average per point x]0.01:0.01:0.99[ (10 000 iterations) at 100 points , we obtain the best fit by Johnson SU distribution , second best by log logistic distribution . This of course requires more points to be made decisive, but both are interesting, especially log logistic because of its many connections and relation to Lambert W function used in solutions of some growth models.

But these things I have to read on...As many others.

Ivars
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Messages In This Thread
RE: Limit of mean of Iterations of f(x)=(ln(x);x>0,ln(-x) x<0) =-Omega constant for all x - by Ivars - 04/06/2008, 06:55 PM

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