Distribution functions

The distribution functions are summarized as follows:

Distribution Distribution function Mean Variance
logistic
0 π2/ 3
normal
0 1
smallest extreme value

(Euler constant)

π2/ 6

Here, γ (in the Mean column) is 0.5772 and π (in the Variance column) is 3.14159.

The distribution function that you select depends on your data. You should select a distribution function that results in a good fit to your data. You can use probability plots and goodness-of-fit tests to compare fits using different distributions. Certain distributions may be used for historical reasons or because they have a special meaning in a discipline.

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