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Exponential family[ред. | ред. код]
Where
let's assume
if so, for
and in exponential family form
for exponential family, moments of distribution could be calculated from deriatives of log normalizer:
First moment (Mean)[ред. | ред. код]
Second moment (Variance)[ред. | ред. код]
Third moment (Skewness)[ред. | ред. код]
Skewness is equal to:
Fourth moment (Kurtosis)[ред. | ред. код]
Kurtosis is equal to: