Are copulas unimodal?

  • Authors:

  • Ioan Cuculescu;Radu Theodorescu

  • Affiliations:

  • Facultatea de matematicã, Universitatea Bucuresti, str. Academiei 14, RO-70109 Bucuresti, Romania;Département de Mathématiques et de Statistique, Université Laval, Sainte-Foy, Québec G1K 7P4, Canada

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2003

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Abstract

Three types of unimodality (central convex, block, and star) are considered and the corresponding sets of unimodal copulas determined. Examples of star unimodal copulas, absolutely continuous, with a nonnull singular part, and even singular, are given. Necessary and sufficient conditions for a diagonal to be the diagonal section of a star unimodal copula are also indicated. Attention is also paid to the Archimedean case.