Most prokaryotic genomes are circular with a single chromosome (called circular genomes), which consist of bacteria and archaea. Orthologous genes (abbreviated as orthologs) are genes directly evolved from an ancestor gene, and can be traced through different species in evolution. Shared orthologs between bacterial genomes have been used to measure their genome evolution. Here, organization of circular genomes is analyzed via distributions of shared orthologs between genomes. However, these distributions are often asymmetric and bimodal, to date, there is no joint distribution to model such data. This motivated us to develop a family of bivariate distributions with generalized von Mises marginals (BGVM) and its statistical inference.