New Families of Wrapped Distributions for Modeling Skew Circular Data

Abstract

We discuss circular distributions obtained by wrapping the classical exponential and Laplace distributions on the real line around the circle. We present explicit forms for their densities and distribution functions, as well as their trigonometric moments and related parameters, and discuss main properties of these laws. Both distributions are very promising as models for asymmetric directional data.

Key Words:

• Angular data
• Asymmetric Laplace distribution
• Bird orientations
• Circular data
• Double exponential distribution
• Wrapped distribution

Mathematics Subject Classification:

• Primary 62H11
• Secondary 62E10

Acknowledgments

We thank the anonymous referee and the editor for their comments.