A Multivariate Extension of the Skew-Unimodal Distributions with Mode-Preserving Property

• Activity Number: 602
• Type: Contributed
• Date/Time: Thursday, August 7, 2014 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Toshihiro Abe*+ and Hironori Fujisawa and Toshikazu Yamaguchi
• Companies: Tokyo University of Science and Institute of Statistical Mathematics and Tokyo University of Science
• Keywords: skewness ; Transformation of scale ; unimodality

Abstract

The skew-symmetric distribution is often-used as a skew-distribution, but it is not always unimodal even if the underlying distribution is unimodal. Recently, another type of skew distribution was proposed using the transformation of scale and it is always unimodal and shows the monotonicity of skewness. In this talk, a multivariate skew distribution is considered using the transformation of scale. The skewness for the multivariate skew distribution is proposed and the monotonicity of skewness is shown. The proposed multivariate skew distribution is more flexible than the conventional multivariate skew-symmetric distributions. Additional properties are also presented, including random number generation, half-distribution, parameter orthogonality, non-degenerated Fisher information, entropy maximization distribution.