[Article] Entropy Analysis of Questionable Text Sources by Example of the Voynich Manuscript

[ReneZ]

The paper is deriving its conclusions entirely from the frequency distribution of single characters.

The first comparison seems to be a visual comparison of the shape of this distribution.
The other two are the regular single-character entropy as it has been used here already (called the Shannon entropy), and the more general Renyi entropy, also applied to single characters.

I had not heard of this before, but what the paper says, combined with a quick look at Wikipedia, clarify what this is about. This is an entropy with a variable parameter alpha, which may run from 0 to infinity.
If alpha = 0 one gets what we have called the H0. If alpha = 1 one gets the Shannon entropy (H1). If alpha goes to infinity, one gets the negative logarithm of the probability of the most frequent character.

Therefore, if two character distributions are similar, also the Renyi entropy as a function of alpha will be similar.

This is what happens in the comparison with plain texts, and this is what the paper shows.

What remains mysterious is that the number of different characters in the various plain texts are extremely large, e.g. 140 for an Italian text. Even counting upper and lower case, the various accented characters, and interpunction, I can't understand where that comes from.