The distribution functions are summarized as follows:
| Distribution | Distribution function | Mean | Variance |
|---|---|---|---|
| logistic |
 |
0 | π2/ 3 |
| normal |
 |
0 | 1 |
| smallest extreme value |
 |
-γ
(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.
