A Study on the Unit-logistic, Unit-Weibull and Topp-Leone Cumulative Sigmoids

In this paper we study the one--sided Hausdorff approximation of the Heaviside step function by a families of Unit-Logistic (UL), Unit-Weibull (UW) and Topp-Leone (TL) cumulative sigmoids. The estimates of the value of the best Hausdorff approximation obtained in this article can be used in practice as one possible additional criterion in ''saturation'' study. Numerical examples are presented using CAS MATHEMATICA.