SUMMARY
The cumulative distribution function (cdf) of the discrete two--parameter bathtub hazard distribution has important role in the fields of population dynamics, reliability analysis and life testing experiments.?Also of interest to the specialists is the task of approximating the Heaviside function by new (cdf) in Hausdorff sense.?We define new activation function and family of new recurrence generated functions and study the ''saturation'' by these families.?In this paper we analyze some intrinsic properties of the new Topp-Leone-G-Family with baseline ''deterministic-type'' (cdf) - (NTLG-DT).?Some numerical examples with real data from Biostatistics, Population dynamics and Signal theory, illustrating our results are given.?It is shown that the study of the two characteristics - "confidential curves" and ''super saturation'' is a must when choosing the right model.?Some related problems are discussed, as an example to the Approximation Theory.