On the extended half–logistic model by H. Bakouch with ”polynomial variable transfer”. Application to approximate the specific ”Data BG COVID–19”

In [1] H. Bakouch consider a G–family of extended cumulative distribution function (cdf): Fa(t)=aG(t)a+1−G(t);a>0, where G(t) is the baseline cdf. In particular case G(t) = 1 − e−kt, k > 0 we find the following Extended–Bakouch Half–Logistic cdf (EBHL-cdf): Fa(t)=a(1−e−kt)a+e−kt.Similar to our previous studies [2]–[4], in this article we will define and analyze in detail the following new family: Fa(t;a0…,an)=a(1−e−F(t))a+e−F(t);F(t)=∑i=0naiti;a0=0.We will call this family the ”Extended–Bakouch Half–Logistic cdf with polynomial variable transfer” (EBHLPVT– cdf). Illustrating our results the following datasets are fitted [5] using CAS MATHEMATICA: ”Data BG Total Cases COVID–19”; ”Data BG Total Deaths COVID–19”.