Most of the existing circular models that appeared in the literature are of unimodal and are not appropriate for fitting bimodal data, such as 13 homing pigeon problems (Jammalamadaka and Sen Gupta 2001) and muscle tissue expression data in genome studies (Clinton et al. 2011). Hence, this chapter is intended to construct bimodal circular models using the technique of offsetting.

The method of transforming a bivariate linear random variable to its directional component is called offsetting, and the respective distribution of directional component is called offset distribution, which is a univariate circular model. Applying this, offset Cauchy distribution (OCD), offset Pearson type II distribution (OP-II) and offset t-distribution (OTD) have been developed in this chapter. Having constructed the new offset circular models, graphs of pdf, cdf and characteristic function of the above distributions are derived.