Vertical Dependency in Sequences of Categorical Random Variables

# Vertical Dependency in Sequences of Categorical Random Variables

## Conclusion

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.

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## References

1. Andrzej Korzeniowski. On correlated random graphs. Journal of Probability and Statistical Science, pages 43–58, 2013.
2. Joseph McKean, Robert Hogg, and Allen Craig. Introduction to Mathematical Statistics. Prentice Hall, 6 edition.
3. Rachel Traylor. A generalized multinomial distribution from dependent categorical random variables. Academic Advances of the CTO, 2017.