On Some Circular Distributions Induced by Inverse Stereographic Projection

Abstract

In earlier studies of circular data, the corresponding probability distributions considered were mostly assumed to be symmetric. However, the assumption of symmetry may not be meaningful for some data. Thus there has been increased interest, more recently, in developing skewed circular distributions. In this article we introduce three skewed circular models based on inverse stereographic projection, originally introduced by Minh and Farnum (2003), by considering three different versions of skewed-t considered in the literature, namely skewed-t by Azzalini (1985), two-piece skewed-t (Fern´andez and Steel, 1998) and skewedt by Jones and Faddy (2003). Shape properties of the resulting circular distributions along with estimation of parameters using maximum likelihood are also discussed in this article. Further, real data sets are used to illustrate the application of the new models. It is found that Azzalini and Jones-Faddy skewed-t versions are good competitors, however, the Jones-Faddy version is computationally more tractable