Premium
A Measure of Dependence Between Two Compositions
Author(s) -
Bergman Jakob,
Holmquist Björn
Publication year - 2012
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2012.00688.x
Subject(s) - mathematics , estimator , confidence interval , correlation ratio , correlation coefficient , statistics , monte carlo method , joint probability distribution , dirichlet distribution , distribution (mathematics) , measure (data warehouse) , mathematical analysis , boundary value problem , database , computer science
Summary We consider the problem of describing the correlation between two compositions. Using a bicompositional Dirichlet distribution, we calculate a joint correlation coefficient, based on the concept of information gain, between two compositions. Numerical values of the joint correlation coefficient are calculated for compositions of two and three components, respectively. We also present an estimator of the joint correlation coefficient for a sample from a bicompositional Dirichlet distribution. Two confidence intervals are presented and we examine their empirical confidence coefficients using a Monte Carlo study. Finally, we apply the estimator to a data set analysing the joint correlation between the 1967 and 1997, and the 1977 and 1997 compositions of the government gross domestic product for the 50 states of the USA and the District of Columbia.