The 
distribution is defined in terms of its distribution
function 
as the solution to the initial value problem
 |
where 
(Savageau 1982, Aksenov and Savageau 2001). It has four free parameters: 
, 
,
, and 
.
The 
distribution is capable of approximating many central and noncentral unimodal univariate
distributions rather well (Voit 1991), but also includes the exponential, logistic,
uniform and linear distributions as special cases. The S distribution derives its
name from the fact that it is based on the theory of S-systems (Savageau 1976, Voit
1991, Aksenov and Savageau 2001).
Aksenov, S. V. "Fitting and Functionals
of the S Distribution." v0.99, 18 June 2002.