View Submission - EcoSta2022

A0540
**Title: **Construction of a circular distribution from a discrete distribution and its extension
**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 at some point and event time measured on a 24-h clock. Such data are called circular data and should be modeled by a distribution defined on the circle, called circular distribution. The trigonometric moments play an important role in characterizing the circular distribution and statistical analysis through the circular distribution. A method is provided for constructing a circular distribution by assuming that the trigonometric moments follow a discrete distribution on the line. The probability density function of the resulting distribution is expressed by using the characteristic function of the discrete distribution. A multivariate extension is also obtained by assuming that the joint trigonometric moments follow a multivariate discrete distribution. Some examples constructed from the proposed method are shown, and fitting examples to real data are given,