Revistes Publicacions URV: SORT - Statistics and Operations Research Transactions> 2006

The importance of being the upper bound in the bivariate family

  • Identification data

    Identifier: RP:2298
    Handle: https://hdl.handle.net/20.500.11797/RP2298
    Authors:
    Cuadras, C. M.
    Abstract:
    Any bivariate cdf is bounded by the Fréchet-Hoeffding lower and upper bounds. We illustrate the importance of the upper bound in several ways. Any bivariate distribution can be written in terms of this bound, which is implicit in logit analysis and the Lorenz curve, and can be used in goodness-of-fit assesment. Any random variable can be expanded in terms of some functions related to this bound. The Bayes approach in comparing two proportions can be presented as the problem of choosing a parametric prior distribution which puts mass on the null hypothesis. Accepting this hypothesis is equivalent to reaching the upper bound. We also present some parametric families making emphasis on this bound.

  • Others:

    URV's Author/s: Cuadras, C. M.
    Abstract: Any bivariate cdf is bounded by the Fréchet-Hoeffding lower and upper bounds. We illustrate the importance of the upper bound in several ways. Any bivariate distribution can be written in terms of this bound, which is implicit in logit analysis and the Lorenz curve, and can be used in goodness-of-fit assesment. Any random variable can be expanded in terms of some functions related to this bound. The Bayes approach in comparing two proportions can be presented as the problem of choosing a parametric prior distribution which puts mass on the null hypothesis. Accepting this hypothesis is equivalent to reaching the upper bound. We also present some parametric families making emphasis on this bound.
    Journal publication year: 2006
    Publication Type: info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/article