The wrapped stable family of distributions as a flexible model for circular data

The four-parameter wrapped stable family of unimodal distributions is considered as a highly flexible model for directional data observed on the unit circle. This family of distributions is capable of modeling both symmetry and asymmetry as well as varying levels of peakedness around the mode and distributional mass around the antimode. The parametrization employed is the circular analog of one for the linear stable family of distributions with properties which make it especially suitable for modeling purposes. The family's characteristic function, trigonometric moments and other standard circular measures are easily derived and have relatively simple forms, but the density can generally be expressed only in terms of a Fourier expansion. Details are given for the method of moments and maximum likelihood approaches to parameter estimation. Likelihood based techniques are used to analyze data on the headings of migrating birds, and the fit of the wrapped stable family compared with those of two finite mixture models.