Abstract
Copulas are important probabilistic tools to model and interpret the correlations of measures involved in real or experimental phenomena. The versatility of these phenomena implies the need for diverse copulas. In this article, we describe and investigate theoretically new two-dimensional copulas based on trigonometric functions modulated by a tuning angle parameter. The independence copula is, thus, extended in an original manner. Conceptually, the proposed trigonometric copulas are ideal for modeling correlations into periodic, circular, or seasonal phenomena. We examine their qualities, such as various symmetry properties, quadrant dependence properties, possible Archimedean nature, copula ordering, tail dependences, diverse correlations (medial, Spearman, and Kendall), and two-dimensional distribution generation. The proposed copulas are fleshed out in terms of data generation and inference. The theoretical findings are supplemented by some graphical and numerical work. The main results are proved using two-dimensional inequality techniques that can be used for other copula purposes.
Highlights
Multidimensional functions called copulas are important in modeling multivariate random variables and understanding their dependence structures
For any integer n, a n-dimensional copula can be defined as a cumulative distribution function defined on
We present and study trigonometric copulas depending on a tuning angle parameter
Summary
Multidimensional functions called copulas are important in modeling multivariate random variables and understanding their dependence structures. The Frank, Gumbel–Hougaard, Ali–Mikhail–Haq, Joe, Farlie–Gumbel–Morgenstern, Clayton, Plackett, Raftery, elliptical, Fréchet, Galambos, and Marshall–Olkin are some of the classical copulas Their definitions are based on motivated transformations of power-polynomial–exponential–logarithmic functions. The inclusion of trigonometric functions in this context confers on the copula some oscillating features that are appropriate to model the correlations into phenomena of periodic, circular, or seasonal nature. They are ideal for analyzing correlations involved in movement data, circular data, and environmental data. We present and study trigonometric copulas depending on a tuning angle parameter.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
