Search Results (5)

The joint probability density function of wind speed and wind direction serves as the mathematical basis for directional wind energy assessment. In this study, a nonparametric joint probability estimation system for wind velocity and direction based on copulas is proposed and empirically investigated in Inner Mongolia, China. Optimal bandwidth algorithms and transformation techniques are used to determine the nonparametric copula method. Various parameter copula models and models without considering dependency relationships are introduced and compared with this approach. The results indicate a significant advantage of employing the nonparametric copula model for fitting joint probability distributions of both wind speed and wind direction, as well as conducting correlation analyses. By utilizing the proposed KDE-COP-CV model, it becomes possible to accurately and reliably analyze how wind power density fluctuates in relation to wind direction. This study reveals the researched region possesses abundant wind resources, with the highest wind power density being highly dependent on wind direction at maximum speeds. Wind resources in selected regions of Inner Mongolia are predominantly concentrated in the northwest and west directions. These findings can contribute to improving the accuracy of micro-siting for wind farms, as well as optimizing the design and capacity of wind turbine generators. Full article

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

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. Full article

Do there exist circular and spherical copulas in ℝ^d? That is, do there exist circularly symmetric distributions on the unit disk in ℝ² and spherically symmetric distributions on the unit ball in ℝ^d, d ≥ 3, whose one-dimensional marginal distributions are uniform? The answer is yes for d = 2 and 3, where the circular and spherical copulas are unique and can be determined explicitly, but no for d ≥ 4. A one-parameter family of elliptical bivariate copulas is obtained from the unique circular copula in ℝ² by oblique coordinate transformations. Copulas obtained by a non-linear transformation of a uniform distribution on the unit ball in ℝ^d are also described, and determined explicitly for d = 2. Full article