In this paper, the author introduces new methods to construct Archimedean copulas. The generator of each copula fulfills the sufficient conditions as regards the boundary and being continuous, decreasing, and convex. Each inverse generator also fulfills the necessary conditions as regards the boundary conditions, marginal uniformity, and 2-increasing properties. Although these copulas satisfy these conditions, they have some limitations. They do not cover the entire dependency spectrum, ranging from perfect negative dependency to perfect positive dependency, passing through the independence state. Even the third copula has a fixed constant Kendall tau measure and fixed values for both the joint CDF and PDF copula, but the generator output changes with the changing value of the dependency parameter. For each copula, the author discusses the derivation, the properties, whether it has a singular part or not, and the Kendall tau measure for dependency. The article shows figures for depicting the generator function, joint CDF, and joint PDF for each copula.
