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Title: A cylindrical distribution whose linear part is heavy-tailed Authors:  Tomoaki Imoto - University of Shizuoka (Japan) [presenting]
Kunio Shimizu - The Institute of Statistical Mathematics (Japan)
Toshihiro Abe - Hosei University (Japan)
Abstract: There exist many examples of heavy-tailed phenomena such as insurance losses and returns in financial data, heavy-precipitation data, and heavy burst of teletransmission and Internet activity. Potential applications are combinations of linear and circular data through 24-hours clock for example as the circular part. If the cylindrical distributions whose linear parts can model only light-tailedness are applied to such data, the estimation and test may be biased by linear large observations, and it leads to wrong results. We propose a cylindrical distribution heavy-tailed for the linear part through a generalized Gamma mixture of Abe-Ley distribution whose linear part is related to a Weibull distribution. The conditional distribution of the linear variable given circular variable is a generalized Pareto distribution and therefore, it might not have any conditional moments, but the mode and median are expressed by closed forms. As an illustrative example, we fit the proposed distribution with likelihood techniques to earthquake data, which consists of the turning angles for epicenters and magnitude during 72 hours before the 2011 Great East Japan Earthquake, and compare the result with those by other cylindrical distributions each of whose linear part model only light-tailedness.