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 .

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 and

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 .

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 and

Ivars