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Distribution and moments of the vector of the maximum of two absolutely continuous random vectors
Institution:1. Department of Statistics, Sungkyunkwan University, 25-2, Sungkyunkwan-ro, Jongno-gu, Seoul, 110-745, Republic of Korea;2. Mathematics Department, Tulane University, 6823 St. Charles Avenue, New Orleans, LA 70118, USA;3. Department of Statistics and Operations Research, UNC at Chapel Hill, CB#3260, Hanes Hall, Chapel Hill, NC 27599, USA;1. Loughborough University, Department of Mathematical Sciences, Loughborough, Leicestershire, LE11 3TU, UK;2. University of Strathclyde, Department of Mathematics and Statistics, Glasgow, G1 1XH, UK;3. School of Economics and Management, Fuzhou University, China;1. Department of Mathematics and Statistics, University of Windsor, Windsor, ON, Canada;2. Department of Mathematics, Brock University, St. Catharines, ON, Canada
Abstract:In this paper, we determine the exact distribution of the vector of the componentwise maximum of two absolutely continuous dependent random vectors and we show that it is a finite mixture of particular skew distributions studied in the literature. The results are detailed when the two vectors are elliptically distributed and some particular cases are discussed. The exact expression of the covariance matrix is obtained in the normal case.
Keywords:Skew distributions  Elliptical distributions  Normal distributions  Mixture  Covariance  Order statistics
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