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Continuous Scaling on a Bivariate Copula

In: Distributions with given Marginals and Moment Problems

Author

Listed:
  • C. M. Cuadras

    (Universitat de Barcelona, Departament d’Estadística)

  • J. Fortiana

    (Universitat de Barcelona, Departament d’Estadística)

Abstract

Cuadras and Fortiana (1993, 1995, 1996b) introduced continuous scaling, an extension of classic metric scaling which gives a decomposition of the variability of a random variable in a countable set of principal axes. (1996a) introduced related metric scaling, a technique to construct a joint distance on a finite set from two marginal distances, with applications to representing categorical data. In this contribution related metric scaling is extended to a bivariate distribution, by introducing dependence between the principal axes obtained from the marginal distances. The formal analogy with the Fréchet class of distributions is explored, and in particular the relations with the product, the lower and the upper bound copulas.

Suggested Citation

  • C. M. Cuadras & J. Fortiana, 1997. "Continuous Scaling on a Bivariate Copula," Springer Books, in: Viktor Beneš & Josef Štěpán (ed.), Distributions with given Marginals and Moment Problems, pages 137-142, Springer.
    • Handle: RePEc:spr:sprchp:978-94-011-5532-8_17
    DOI: 10.1007/978-94-011-5532-8_17
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