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Title: Simple constructions of joint distributions with circular marginal Authors:  Tomoaki Imoto - University of Shizuoka (Japan) [presenting]
Abstract: In diverse scientific fields, a data sample is often represented as a point in the circumference of a unit circle. Typical examples are wind direction and event time measured on a 24-hour clock. Such data are called circular data and should be modeled by a distribution defined on the circle, called circular distribution. In many cases, circular observation appears with the other circular or linear observations like wind directions at the different places, distance of animal movement and its direction, pass position and direction in soccer game and so on. For modeling and analyzing such datasets, distributions on the torus and cylinder, called toroidal distribution and cylindrical distribution, are useful tools. Several methods for constructing such distributions have been considered; maximum entropy method, trivariate reduction method, wrapping method, specified conditionals or marginals methods. Simple methods for constructing joint distributions with circular marginal are proposed as methods of specifying marginal distributions. The constructed probability density function is expressed without additional normalizing constants, and its trigonometric moments and correlation measure are expressed by simple forms, which help characterize the distribution. Other researches about estimation and application for fitting real data are also shown.