Abstract

In earlier studies of circular data, mostly circular distributions were considered and many biological data sets were assumed to be symmetric. However, presently interest has increased for skewed circular distributions as the assumption of symmetry may not be meaningful for some data. This thesis introduces three skewed circular models based on inverse stereographic projection, introduced by Minh and Farnum (2003), by considering three different versions of skewed-t considered in the literature, namely Azzalini skewed-t, two-piece skewed-t and Jones and Faddy skewed-t. Shape properties of the resulting distributions along with estimation of parameters using maximum likelihood are discussed in this thesis. Further, three real data sets (Bruderer and Jenni, 1990; Holzmann et al., 2006; Fisher, 1993) are used to illustrate the application of the new model and its extension to finite mixture modelling. Goodness of fit of the new distributions is studied using maximum log-likelihood and Akaike information criterion and chi-square values. It is found that Azzalini and Jones-Faddy skewed-t versions are good competitors; however the Jones-Faddy version is computationally more tractable.