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Logistic Normal Distribution

Logistic-normal distributions:

The logistic transformation applied to a d-dimensional normal distribution produces a distribution over the d-dimensional simplex which can sensibly be termed a logistic-normal distribution.

Following is a diagram from Brendam O’Connor.



For example, when you throwing an uniformity distributed coin.


The probability of getting a head is p(x)= (Chances for) / (Total chances) .


The odds is given as:  (Chances for) : (Chances against) . where (total chances) = (Chances for)  + (Chances against)


Logistic-normal distributions:Some properties and uses. Biometrika(1980) By J. AITCHISON AND S.M.SHEN

So, what do you think ?