Multivariate Order Statistics Induced by Ordering Linear Combinations of Components of Multivariate Elliptical Random Vectors

DOI10.1007/978-3-030-42196-0_3OpenAlexW3048383411MaRDI QIDQ5050404

Mehrdad Naderi, Roohollah Roozegar, Ahad Jamalizadeh, Narayanaswamy Balakrishnan

Publication date: 15 November 2022

Published in: Emerging Topics in Statistics and Biostatistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-42196-0_3

zbMATH Keywords

order statisticslogistic distributionconditional expectationcovariance matrixprobability density functionjoint distributionstochastic representationmixture distributionmultivariate normal distributionskew-elliptical distributionQ-Q plotelliptical distributionmarginal distributionskew-symmetric distributioncumulative distribution functionconcomitants of order statisticstruncated distributionmultivariate unified skew-\(t\) distributionmultivariate unified skew-elliptical distributionmultivariate unified skew-normal distributioninduced order statisticsmoments of distributionsquare error lossgeneralized Shapiro-Wilk testconditional distribution coherencedensity generator functionenergy testmaximized likelihood estimationmultivariate student-\(t\) distributionmultivariate truncated normal distributionmultivariate truncated student-\(t\) distribution

Mathematics Subject Classification ID

Applications of statistics to biology and medical sciences; meta analysis (62P10)

Uses Software

• mvShapiroTest

Cites Work

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• A note on moments of variables summing to normal order statistics
• A new test for multivariate normality
• Multivariate order statistics via multivariate concomitants
• On the theory of elliptically contoured distributions
• Skewed multivariate models related to hidden truncation and/or selective reporting. With discussion and a rejoinder by the authors.
• On a class of multivariate distributions closed under concomitance of order statistics
• On the Unification of Families of Skew-normal Distributions
• The multivariate skew-normal distribution
• Prediction based on linear combinations of order statistics and bivariate concomitants in the case of multivariate elliptical distributions

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