The values of y_n and s_n depend only on the number of elements in the sample. In order to compute it, you first have to compute the Average Recurrence Interval (T) for every element of the sample (i.e. for every m from 1 to n), based on a plotting position formula (table 3).

For the n values of T, you can compute the corresponding Gumbel Variate y (again n different values).

The mean value of y is y_n, the standard deviation of y is s_n.

I hope you find it useful

In my perspective, it is related to the number of your data. As far as my experience helps, when I was working with software of the Easy Fit for assessment of statistical distributions in the flood project, by change of numbers of elements, the amount of these parameters changed.

Thank a lot !