Vertical Dependency in Sequences of Categorical Random Variables

# Vertical Dependency in Sequences of Categorical Random Variables

This paper has extended the concept of dependent random sequences first put forth in the works of Korzeniowski [1] and Traylor [3] and developed a generalized class of vertical dependency structures. The sequential dependency structure was studied extensively, and a formula for the cross-covariance obtained. The class of dependency generators was defined and shown to always produce a unique dependency structure for any $\alpha \in \mathscr{C}_{\delta}$ in which the a sequence of categorical random variables under that $\alpha$ is identically distributed but dependent. We provided a graphical interpretation of this class, and illustrated with several key examples.