A stochastic ordering based on the canonical transformation of skew-normal vectors

• Jorge M. Arevalillo ^[1] ; Hilario Navarro ^[1]
  1. [1] University Nacional Educación a Distancia (UNED)
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 28, Nº. 2, 2019, págs. 475-498
• Idioma: inglés
• DOI: 10.1007/s11749-018-0583-5
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• Resumen

  • In this paper, we define a new skewness ordering that enables stochastic comparisons for vectors that follow a multivariate skew-normal distribution. The new ordering is based on the canonical transformation associated with the multivariate skew-normal distribution and on the well-known convex transform order applied to the only skewed component of such canonical transformation. We examine the connection between the proposed ordering and the multivariate convex transform order studied by Belzunce et al. (TEST 24(4):813–834, 2015). Several standard skewness measures like Mardia’s and Malkovich–Afifi’s indices are revisited and interpreted in connection with the new ordering; we also study its relationship with the J-divergence between skew-normal and normal random vectors and with the Negentropy. Some artificial data are used in simulation experiments to illustrate the theoretical discussion; a real data application is provided as well.