Two nested families of skew-symmetric circular distributions

In this paper, we introduce two new flexible families of unimodal circular distributions obtained by wrapping onto the unit circle two recently explored heavytailed distributions defined on the real line. The first, the four-parameter wrapped normal–Laplace distribution, is nested within the second, the five-parameter wrapped generalized normal–Laplace distribution. Both families contain the wrapped normal and wrapped Laplace and generalized Laplace distributions as special cases. Stochastic models for the genesis of these new distributions, which may be useful in identifying situations in which they are likely to occur, are developed. The basic properties of the new distributions are derived and model fitting by maximum likelihood discussed. Examples which illustrate fitting the two distributions to exact and grouped data are presented.