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The distribution of the relative arc density of a family of interval catch digraph based on uniform data


  • Elvan Ceyhan



We study a family of interval catch digraph called proportional-edge proximity catch digraph (PCD) which is also a special type of intersection digraphs parameterized with an expansion and a centrality parameter. PCDs are random catch digraphs that have been developed recently and have applications in classification and spatial pattern analysis. We investigate a graph invariant of the PCDs called relative arc density. We demonstrate that relative arc density of PCDs is a U-statistic and using the central limit theory of U-statistics, we derive the (asymptotic) distribution of the relative arc density of proportional-edge PCD for uniform data in one dimension. We also determine the parameters for which the rate of convergence to asymptotic normality is fastest. Copyright Springer-Verlag 2012

Suggested Citation

  • Elvan Ceyhan, 2012. "The distribution of the relative arc density of a family of interval catch digraph based on uniform data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(6), pages 761-793, August.
  • Handle: RePEc:spr:metrik:v:75:y:2012:i:6:p:761-793
    DOI: 10.1007/s00184-011-0351-y

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    References listed on IDEAS

    1. Ceyhan, Elvan & Priebe, Carey E., 2005. "The use of domination number of a random proximity catch digraph for testing spatial patterns of segregation and association," Statistics & Probability Letters, Elsevier, vol. 73(1), pages 37-50, June.
    2. Priebe, Carey E. & DeVinney, Jason G. & Marchette, David J., 2001. "On the distribution of the domination number for random class cover catch digraphs," Statistics & Probability Letters, Elsevier, vol. 55(3), pages 239-246, December.
    3. Priebe, Carey E. & Solka, Jeffrey L. & Marchette, David J. & Clark, B. Ted, 2003. "Class cover catch digraphs for latent class discovery in gene expression monitoring by DNA microarrays," Computational Statistics & Data Analysis, Elsevier, vol. 43(4), pages 621-632, August.
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