<A HREF="http://interstat.statjournals.net/YEAR/2003/articles/0302003.pdf">A Remark on the Convolution of the Generalised Logistic Random Variables</A>, Matthew Oladejo Ojo (2003).

Probability density function $f(x)$ for each of $n$ independent random variables gives the probability distribution $f_n(y)$ for the sum:

<IMG SRC="http://ilorentz.org/beenakker/MO/logistic.png">