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On the Variety of Shapes in Digital Trees

Author

Listed:
  • Jeffrey Gaither

    (The Ohio State University)

  • Hosam Mahmoud

    (The George Washington University)

  • Mark Daniel Ward

    (Purdue University)

Abstract

We study the joint distribution of the number of occurrences of members of a collection of nonoverlapping motifs in digital data. We deal with finite and countably infinite collections. For infinite collections, the setting requires that we be very explicit about the specification of the underlying measure-theoretic formulation. We show that (under appropriate normalization) for such a collection, any linear combination of the number of occurrences of each of the motifs in the data has a limiting normal distribution. In many instances, this can be interpreted in terms of the number of occurrences of individual motifs: They have a multivariate normal distribution. The methods of proof include combinatorics on words, integral transforms, and poissonization.

Suggested Citation

  • Jeffrey Gaither & Hosam Mahmoud & Mark Daniel Ward, 2017. "On the Variety of Shapes in Digital Trees," Journal of Theoretical Probability, Springer, vol. 30(4), pages 1225-1254, December.
    • Handle: RePEc:spr:jotpro:v:30:y:2017:i:4:d:10.1007_s10959-016-0700-x
    DOI: 10.1007/s10959-016-0700-x
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    References listed on IDEAS

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    1. Mohan Gopaladesikan & Hosam Mahmoud & Mark Daniel Ward, 2014. "Asymptotic Joint Normality of Counts of Uncorrelated Motifs in Recursive Trees," Methodology and Computing in Applied Probability, Springer, vol. 16(4), pages 863-884, December.
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