On the Extreme Points of the Set of All 2xn Bivariate Positive Quadrant Dependent Distributions with Fixed Marginals and Some Applications.

Abstract

The set of all bivariate distributions with support contained in ((i.j); i = 1,2 and j = 1,2..., n) which are positive quadrant dependent is a convex set. In the paper, an algebraic method is presented for the enumeration of all extreme points of this convex set. Certain measures of dependence, including Kendall's tau, are shown to be affine functions on this convex set. This property of being affine helps us to evaluate the asymptotic power of tests based on these measures of dependence for testing the hypothesis of independence against strict positive quadrant dependence. Keywords: Multivariate analysis; Asymptotic; Random variables; Probability distribution functions.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1987
Accession Number
ADA186316

Entities

People

  • K. Subramanyam
  • M. Bhaskara Rao

Organizations

  • University of Pittsburgh

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Air Force
  • Computations
  • Convex Sets
  • Distribution Functions
  • Equations
  • Governments
  • Inequalities
  • Multivariate Analysis
  • Numbers
  • Probability
  • Probability Distribution Functions
  • Probability Distributions
  • Quadrants
  • Random Variables
  • Theorems
  • United States Government
  • Universities

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Regression Analysis.