Based on what I found here:
Entropy of Log-Poisson process
The distribution of values including far rare jumps based on change of sign with mod under logarithm has to be log-Poisson or negative log-Poisson, because the mean value of such infinite iteration is entropy of such process \( S= -\Omega \).
Unofortunately, I could not find the parameters of log-Poisson distribution (mean, variance, skewness, kurtosis etc.) to compare with my numeric results.
The hidden mean of 2 such distributions, log Poisson and negative log Poisson is \( e^{+\Omega}= 1,7632..= 1/\Omega \) and \( e^{-\Omega}= \Omega=0,567143.. \)
Ivars
Entropy of Log-Poisson process
The distribution of values including far rare jumps based on change of sign with mod under logarithm has to be log-Poisson or negative log-Poisson, because the mean value of such infinite iteration is entropy of such process \( S= -\Omega \).
Unofortunately, I could not find the parameters of log-Poisson distribution (mean, variance, skewness, kurtosis etc.) to compare with my numeric results.
The hidden mean of 2 such distributions, log Poisson and negative log Poisson is \( e^{+\Omega}= 1,7632..= 1/\Omega \) and \( e^{-\Omega}= \Omega=0,567143.. \)
Ivars