A0609
Title: New family of a toroidal distribution whose marginal and conditional distributions are skewed
Authors: Tomoaki Imoto - University of Shizuoka (Japan) [presenting]
Abstract: Circular distribution is used for analyzing data whose observations are represented as points in the circumference of a unit circle, which is called circular data. In many cases, circular observations are made on two or more circular variables, like a combination of the directions of the wind at some points. For modelling and analyzing such data, distribution on the torus, called toroidal distribution, is a useful tool. The family of a sine-correlated distribution is a simple model, and its marginal distributions can be specified by any circular distribution. However, the circular correlation structure is too weak, and therefore, its applications will be restricted. A new method is proposed for constructing a toroidal distribution whose correlation structure is strong. The marginal and conditional distributions are skewed distributions, and the trigonometric moments are expressed in a simple form. From the expression, the role of parameters in the constructed distribution will be found. The illustrative example of fitting real data to the proposed distribution is also shown.
