Increasing directionally convex orderings of random vectors having the same copula, and their use in comparing ordered data

  • Authors:

  • Narayanaswamy Balakrishnan;Félix Belzunce;Miguel A. Sordo;Alfonso Suárez-Llorens

  • Affiliations:

  • Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1;Dpto. Estadística e Investigación Operativa, Universidad de Murcia, 30100 Espinardo (Murcia), Spain;Dpto. Estadística e Investigación Operativa, Universidad de Cádiz, 11002 Cádiz, Spain;Dpto. Estadística e Investigación Operativa, Universidad de Cádiz, 11002 Cádiz, Spain

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2012

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Abstract

In this paper, we establish some results for the increasing convex comparisons of generalized order statistics. First, we prove that if the minimum of two sets of generalized order statistics are ordered in the increasing convex order, then the remaining generalized order statistics are also ordered in the increasing convex order. This result is extended to the increasing directionally convex comparisons of random vectors of generalized order statistics. For establishing this general result, we first prove a new result in that two random vectors with a common conditionally increasing copula are ordered in the increasing directionally convex order if the marginals are ordered in the increasing convex order. This latter result is, of course, of interest in its own right.