Re: why use log in statistics?

If frequencies of words in texts are evaluated,
than frequencies of words used once, twice, and so on,
are modeled by the lognormal distribution (except that there are more
rare words than expected).
Suppose that texts are generated as the products n^m, where n is the
set of all signs on your keyboard n = (` + ~ .. + q + Q ...+ / + ?)
and m is the length of the text. Beween all, mostly nonsense, generated
strings of sufficient length will be also the string "all generated
strings".
We deal with products. To transform them into sums, we need logarithm.
These can have different bases: natural, binary, decadic. A special
base is the unary: alog_(1)a = 1 or log(aa) = a + a.
A text can be transformed into a matrix, a = (1,..,0), z = (0,...,1),
writing consecutive symbols as its rows. With these matrices, many
operations can be performed (permutations, finding quadratic forms,
additions and subtractions).
kunzmilan

.

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