A Collection of New Trigonometric- and Hyperbolic-FGM-Type Copulas

Copula analysis was created to explain the dependence of two or more quantitative variables. Due need for in-depth data involving complex variable relationships, there is always a new copula models with original features. As modern example, circular periodic types, trigonometric copulas are particularly attractive and recommended. This is, however, an underexploited topic. In this article, we propose collection eight hyperbolic copulas, four based on sine function others tangent function, all derived from construction famous Farlie–Gumbel–Morgenstern copula. addition their functionalities, proposed have feature depending three parameters complementary roles: one parameter; shape last can be viewed as angle parameter. our main findings, each determine wide range admissible values these parameters. Subsequently, capabilities, features, functions thoroughly examined. The shapes some illustrated graphically. Theoretically, symmetry in general, stochastic dominance, quadrant dependence, tail Archimedean nature, correlation measures, inference investigated. Some help figures. On other hand, two-dimensional inequalities established may separate interest.