A New Class of Multivariate Power Distributions

• Activity Number: 655
• Type: Contributed
• Date/Time: Thursday, August 4, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Hassan Elsalloukh*+ and Howraa Al-Mousawi and Thomas McMillan
• Companies: University of Arkansas at Little Rock and University of Arkansas at Little Rock and University of Arkansas at Little Rock
• Keywords: Epsilon skew Laplace distribution ; asymmetric skew distributions ; multivariate distributions ; heavy tail distributions

Abstract

The multivariate normal distribution plays an important role in the analysis of multivariate data, but there still remains many important problems where real data do not follow the normal distribution. When the analysis of data indicates that the normality assumption is violated, more flexible models should be considered as an alternative to present the data. In this article, we develop a new distribution, the Multivariate Epsilon Skew Laplace Distribution (MESL). The MESL is an asymmetric distribution that can handle both symmetric, asymmetric, and heavy tail data. The bivariate case is provided to clarify and demonstrate theMESL distribution. Properties of theMESL distribution are developed, in particular, the moment generating function, the characteristic function, the mean, and the variance.