It is shown that a general parametric functional generates the conditional and joint probabilities of event pairs when the order within paired events is irrelevant. The parameters represent affinities or associations between single events. If the marginal probabilities of the single events are known, then these parameters specify a hypersurface on which all the joint probabilities of event pairs must lie. Examples are presented, and applications in probability, ecology, epidemiology, genetics, and distribution theory are offered.
ASJC Scopus subject areas
- Statistics and Probability
- Modeling and Simulation
- Biochemistry, Genetics and Molecular Biology(all)
- Immunology and Microbiology(all)
- Agricultural and Biological Sciences(all)
- Applied Mathematics