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Models for circular-linear and circular-circular data constructed from circular distributions based on nonnegative trigonometric sums. (English) Zbl 1134.62030
Summary: R. A. Johnson and T. E. Wehrly [J. Am. Stat. Assoc. 73, 602–606 (1978; Zbl 0388.62059)] and T. E. Wehrly and R. A. Johnson [Biometrika 67, 255–256 (1980; Zbl 0431.62056)] have shown one way to construct the joint distribution of a circular and a linear random variable, or the joint distribution of a pair of circular random variables from their marginal distributions and the density of a circular random variable, which in this article is referred to as joining circular density. To construct flexible models, it is necessary that the joining circular density be able to present multimodality and/or skewness in order to model different dependence patterns. The present author [Biometrics 60, No. 2, 499–503 (2004; Zbl 1274.62352)] constructed circular distributions based on nonnegative trigonometric sums that can present multimodality and/or skewness. Furthermore, they can be conveniently used as a model for circular-linear or circular-circular joint distributions.
In the current work, joint distributions for circular-linear and circular-circular data constructed from circular distributions based on nonnegative trigonometric sums are presented and applied to two data sets, one for circular-linear data related to air pollution patterns in Mexico City and the other for circular-circular data related to the pair of dihedral angles between consecutive amino acids in a protein.

MSC:
62H11 Directional data; spatial statistics
62H10 Multivariate distribution of statistics
62P12 Applications of statistics to environmental and related topics
62P10 Applications of statistics to biology and medical sciences; meta analysis
92C40 Biochemistry, molecular biology
Software:
CircStats; circular
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