Construction of New Bivariate Semilinear Copulas Based on the Ali–Mikhail–Haq, Farlie–Gumbel–Morgenstern and Plackett Families

Copulas are quite a popular, flexible, and useful tool for multivariate modeling in many fields of applications, including finance and insurance, actuarial sciences, biomedical studies, geostatistics, and hydrology. In this paper, we use the concept of diagonal function to build new bivariate copulas based on the well known and important Ali–Mikhail–Haq (AMH), Farlie–Gumbel–Morgenstern (FGM) and Plackett families. We also study some dependence properties of the newly constructed semilinear copulas, namely, the Spearman’s Formula: see text coefficient. In particular, we find that the range of this rank correlation coefficient varies between weak and moderate values for the transformed AMH and FGM families, although it varies between moderate and strong values for the transformed Plackett families. Moreover, in all cases, the Spearman’s Formula: see text coefficient reaches negative and positive values. Finally, we present a synthetic data generation algorithm, as well as a classical method of estimation of the copula association parameter Formula: see text for each of the six transformed bivariate families.