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Title: Pareto type probability distribution for cylindrical data Authors:  Tomoaki Imoto - University of Shizuoka (Japan) [presenting]
Kunio Shimizu - The Institute of Statistical Mathematics (Japan)
Toshihiro Abe - Nanzan University (Japan)
Abstract: A probability distribution on the cylinder, or cylindrical distribution provides a bivariate distribution with linear and circular random variables. We propose a cylindrical distribution which has a heavy-tailed linear marginal distribution. Its conditional distribution of the linear variable given circular variable is a generalized Pareto distribution, so it might not have any conditional moments. However, since the conditional mode and median are expressed by the closed forms, we can use these indices to represent the relation between the linear and circular variables. The circular marginal distribution is a wrapped Cauchy distribution and conditional distribution of the circular variable given linear variable is the family of Jones and Pewsey distribution. These properties leads to the application for the cylindrical data whose linear variable might have large values and circular variable is symmetric. As an example of applications, we fit the proposed distribution to the seismic magnitude and sequences of epicenter data and compare the result with that by other cylindrical distribution which has a light-tailed linear marginal distribution.