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Models for circular-linear and circular-circular data constructed from circular distributions based on nonnegative

J J Fernández-Durán¹

¹Department of Statistics, Instituto Tecnológico Autónomo de México, Río Hondo No. 1, Col. Tizapán San Angel, C.P. 01000, México D.F., México. jfdez@itam.mx

|August 11, 2007

Summary

This study introduces flexible joint distributions for circular-linear and circular-circular data using nonnegative trigonometric sums. These models capture complex dependence patterns, including multimodality and skewness, with applications in environmental science and bioinformatics.

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Area of Science:

Statistics
Bioinformatics
Environmental Science

Background:

Existing methods for constructing joint distributions of circular and linear variables (circular-linear) or pairs of circular variables (circular-circular) have limitations in flexibility.
Flexible models require the joining circular density to accommodate multimodality and skewness for diverse dependence patterns.

Purpose of the Study:

To present and apply joint distributions for circular-linear and circular-circular data using nonnegative trigonometric sums.
To demonstrate the utility of these flexible models in real-world applications.

Main Methods:

Construction of joint distributions based on circular distributions derived from nonnegative trigonometric sums.
Application of these methods to two distinct datasets: air pollution data (circular-linear) and protein structure data (circular-circular).

Main Results:

The developed methods successfully model complex dependence structures in both circular-linear and circular-circular data.
The models exhibit flexibility in capturing multimodality and skewness, essential for realistic data representation.

Conclusions:

Nonnegative trigonometric sums provide a powerful framework for constructing flexible joint distributions in circular statistics.
These distributions offer valuable tools for analyzing complex dependencies in environmental and biological data.