S Distribution

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).

REFERENCES:

Aksenov, S. V. "Fitting and Functionals of the S Distribution." v0.99, 18 June 2002. https://aksenov.freeshell.org/sdist.html.

Aksenov, S. V. and Savageau, M. A. "Statistical Inference and Modeling with the S Distribution." 17 Dec 2001. https://arxiv.org/abs/physics/0112046.

Savageau, M. A. Biochemical Systems Analysis: A Study of Function and Design in Molecular Biology. Cambridge, MA: Addison-Wesley, 1976.

Savageau, M. A. "A Suprasystem of Probability Distributions." Biom. J. 24, 323-330, 1982.

Voit, E. O. (Ed.). Canonical Nonlinear Modeling: S-System Approach to Understanding Complexity. New York: Van Nostrand Reinhold, 1991.

Voit, E. O. and Savageau, M. A. "Analytical Solutions to a Growth Equation." J. Math. Anal. Appl. 103, 380-386, 1984.