F-Independence and Null Correlation of Continuous, Bounded-Sum, Positive Variables
J. N. Darroch, Ian James · Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1974
Summary The concept of F-independence, previously discussed (Darroch, 1971) for integer-valued variables, is here developed for r continuous, positive variables whose sum is bounded. Part of the theory parallels the theory for integer-valued variables and differs only in some additional mathematical questions which are encountered. Several topics discussed in this paper are special to continuous variables. These include the relationship of neutrality, of the Dirichlet distribution and of the beta distribution to F-independence. These relationships are effected through the concept of proportion-invariance. The paper concludes with an account of some correlation theory for bounded-sum variables.