Abstract
In this paper, we propose a new method for constructing a toroidal distribution from independent circular distributions by specifying marginal distributions. The constructed probability density function is expressed without additional normalizing constants, and its conditional distributions belong to the family of sine-skewed circular distributions. The simple expressions for trigonometric moments, especially for correlation measures, help characterize the proposed model. Maximum likelihood estimation is computationally tractable, and the correlation parameter is orthogonal to the location and concentration parameters when the marginal distributions are symmetric. Two illustrative applications are shown comparing genome structures between paired bacteria.
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