The generalized symmetric Laplace distribution on the sphere
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- 作者：Hai-Yen Siew ; Kunio Shimizu
- 关键词：Cardioid distribution ; Directional statistics ; E– ; M-algorithm ; Normal mixture ; Von Mises– ; Fisher distribution
- 刊名：Statistical Methodology
- 出版年：2008
- 出版时间：November 2008
- 年：2008
- 卷：5
- 期：6
- 页码：487-501
- 全文大小：650 K
文摘
A distribution on the unit sphere is generated by conditioning a normal mixture distribution with an inverse gamma distributed weighting function. It can be regarded as the generalized symmetric Laplace distribution on the unit sphere. The density involves a modified Bessel function of the third kind which can be approximated by other simpler functions in certain limiting cases. As a consequence, the von Mises–Fisher, cardioid and Jones–Pewsey distributions are limiting cases of the new distribution. No closed form expressions exist for the roots of the likelihood equations. However, given the normal mixture structure of the distribution, we propose an E–M-algorithm-based approach for finding the maximum-likelihood estimates of the parameters which assumes the weights in the mixture to be missing data. The modeling capabilities of the proposed distribution are illustrated by fitting it and some of its competitors to two circular data sets.