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Title: Discretized circular distribution Authors:  Tomoaki Imoto - University of Shizuoka (Japan) [presenting]
Kunio Shimizu - The Institute of Statistical Mathematics (Japan)
Abstract: In many diverse scientific fields, there often appear data considered as points on a unit circle, called circular data, such as wind directions at a monitoring site, vanishing angles of birds from a starting point, intensive care unit arrival times on the 24-hour clock. For modeling circular data, many continuous circular distributions (CCDs) have been constructed using several methods such as projection, conditioning and maximizing entropy and so on. In practice, for different reasons, observed values are discretized. We propose a method to construct a discrete circular distribution (DCD) from a CCD. The pmf is defined to take the normalized values of the pdf at some pre-fixed equidistant points on the circle. When the pdf is represented by a Fourier series, the constructed pmf is concisely expressed by the cosine moments of the CCD. Simulation studies show that DCDs outperform the corresponding CCDs in modeling grouped circular data, and that minimum chi-square estimation is better than maximum likelihood estimation when the number of groups on the circle is not large.