I obtained the distributions around of integer positive iterations of these functions using module each time argument gets negative.

The distributions are symmetric against ordinate axis, point x=0, but they overlap. I am not sure of the type of the distributions, nor how does standard accuracy of Excel influence them- obviously, the values float away from where they should be, but, since we obtain correctly the mean values may be the distribution principially is the same regardless of accuracy given enough iterations are made. They seemed to be log normal but they are not. Weibull is too difficult for me to compare to data set.

Anyway, here are histograms- probability density functions and data parameters from excel:

ln(mod(x)):

Mean -0,569047639

Standard Error 0,012051586

Median -0,372148702

Mode #N/A

Standard Deviation 1,206784434

Sample Variance 1,456562737

Kurtosis 2,838543218

Skewness -1,189194674

Range 11,75801951

Minimum -9,512327352

Maximum 2,245692157

ln(mod(1/x)):

Mean 0,568939972

Standard Error 0,011986562

Median 0,372020783

Mode #N/A

Standard Deviation 1,205767153

Sample Variance 1,454070305

Kurtosis 2,858638726

Skewness 1,190184673

Range 11,83018032

Minimum -2,251410718

Maximum 9,578769599

In principle, all parameters are the same, just the ones who can, change sign. Obviously, location parameter needs to be added (its NOT 0) and mean and maximum does not coincide.

the value of median is Interesting. Could it be ? Probably not.

The distirbution looks a little like this:

log Weibull Ditribution

But ... I have a feeling that this distribution has to be iterated (tetrated?) as well to obtain some limit distribution, since I have been applying ln many times to those variables x which were quite regularly distributed at the beginning and obtained some peculiar chaos.

Ivars

The distributions are symmetric against ordinate axis, point x=0, but they overlap. I am not sure of the type of the distributions, nor how does standard accuracy of Excel influence them- obviously, the values float away from where they should be, but, since we obtain correctly the mean values may be the distribution principially is the same regardless of accuracy given enough iterations are made. They seemed to be log normal but they are not. Weibull is too difficult for me to compare to data set.

Anyway, here are histograms- probability density functions and data parameters from excel:

ln(mod(x)):

Mean -0,569047639

Standard Error 0,012051586

Median -0,372148702

Mode #N/A

Standard Deviation 1,206784434

Sample Variance 1,456562737

Kurtosis 2,838543218

Skewness -1,189194674

Range 11,75801951

Minimum -9,512327352

Maximum 2,245692157

ln(mod(1/x)):

Mean 0,568939972

Standard Error 0,011986562

Median 0,372020783

Mode #N/A

Standard Deviation 1,205767153

Sample Variance 1,454070305

Kurtosis 2,858638726

Skewness 1,190184673

Range 11,83018032

Minimum -2,251410718

Maximum 9,578769599

In principle, all parameters are the same, just the ones who can, change sign. Obviously, location parameter needs to be added (its NOT 0) and mean and maximum does not coincide.

the value of median is Interesting. Could it be ? Probably not.

The distirbution looks a little like this:

log Weibull Ditribution

But ... I have a feeling that this distribution has to be iterated (tetrated?) as well to obtain some limit distribution, since I have been applying ln many times to those variables x which were quite regularly distributed at the beginning and obtained some peculiar chaos.

Ivars