Our main goal in this article is to present the approaches and examples of three functions in R consist of optim, nleqslv and maxLik function to detect the optimization solution of the estimating function in the regression models. We then compare the results with numerous sample sizes (n=150, 300 and 500), the execution time of R code, as well as Normal Q - Q plots of three approaches through some of regression models such as the zero-inflated Binomial (ZIB) regression model, logistic regression model, the zero-inflated Poisson (ZIP) regression model and the zero-inflated Bernoulli (ZIBer) regression model. Finally, we discuss potential research directions in the coming times.  This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.