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Normal Limiting Distribution of the Size of Binary Interval Trees

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  • Jie Liu
  • Yang Yang

Abstract

The limiting distribution of the size of binary interval tree is investigated. Our illustration is based on the contraction method, and it is quite different from the case in one-sided binary interval tree. First, we build a distributional recursive equation of the size. Then, we draw the expectation, the variance, and some high order moments. Finally, it is shown that the size (with suitable standardization) approaches the standard normal random variable in the Zolotarev metric space.

Suggested Citation

  • Jie Liu & Yang Yang, 2015. "Normal Limiting Distribution of the Size of Binary Interval Trees," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-9, October.
    • Handle: RePEc:hin:jnlmpe:756548
    DOI: 10.1155/2015/756548
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