# Vertical Dependency in Sequences of Categorical Random Variables

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## 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

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