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

Any bivariate cdf is bounded by the Fr ´echet-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-...

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Bibliographic Details
Author: Cuadras, C.M. (Carlos Maria)
Format: article
Publication Date:2006
Country:España
Institution:Universitat Politècnica de Catalunya (UPC)
Repository:UPCommons. Portal del coneixement obert de la UPC
Language:English
OAI Identifier:oai:upcommons.upc.edu:2099/3788
Online Access:https://hdl.handle.net/2099/3788
Access Level:Open access
Keyword:Distribution (Probability theory)
Multivariate analysis
Inference
Distribució (Teoria de la probabilitat)
Anàlisi multivariable
Inferència
Classificació AMS::60 Probability theory and stochastic processes::60E Distribution theory
Classificació AMS::62 Statistics::62H Multivariate analysis
Classificació AMS::62 Statistics::62F Parametric inference
Description
Summary:Any bivariate cdf is bounded by the Fr ´echet-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.