# The importance of being the upper bound in the bivariate family.

SORT (2006)

- Volume: 30, Issue: 1, page 55-84
- ISSN: 1696-2281

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topCuadras, Carles M.. "The importance of being the upper bound in the bivariate family.." SORT 30.1 (2006): 55-84. <http://eudml.org/doc/41619>.

@article{Cuadras2006,

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.},

author = {Cuadras, Carles M.},

journal = {SORT},

keywords = {Distribuciones bivariantes; Acotación; Tablas de contingencia; Análisis de correlación; Inferencia bayesiana; Hoeffding's lemma; Fréchet-Hoeffding bounds; given marginals; diagonal expansion; logit analysis; goodness-of-fit; Lorenz curve; Bayes test in tables},

language = {eng},

number = {1},

pages = {55-84},

title = {The importance of being the upper bound in the bivariate family.},

url = {http://eudml.org/doc/41619},

volume = {30},

year = {2006},

}

TY - JOUR

AU - Cuadras, Carles M.

TI - The importance of being the upper bound in the bivariate family.

JO - SORT

PY - 2006

VL - 30

IS - 1

SP - 55

EP - 84

AB - 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.

LA - eng

KW - Distribuciones bivariantes; Acotación; Tablas de contingencia; Análisis de correlación; Inferencia bayesiana; Hoeffding's lemma; Fréchet-Hoeffding bounds; given marginals; diagonal expansion; logit analysis; goodness-of-fit; Lorenz curve; Bayes test in tables

UR - http://eudml.org/doc/41619

ER -