Kies Cumulative Distribution Function: Reaction Network Analysis and Related Problems

The Kies probability model [1] was proposed as an alternative to the extended Weibull models as it provides a more efficient fit to some real-life data sets in comparison to the aforementioned models. In the present article, it has first been shown that the dynamic Kies model is generated by a specific framework of chemical reaction networks. We will also discuss some properties of the family by Kies. Precise bounds for the Hausdorff distance between the Heaviside step function and the considered sigmoid are also given. We also define a hypothetical family of generalized Kies CDF. Some computational examples using CAS Mathematica are presented.