The distribution of the relative arc density of a family of interval catch digraph based on uniform data
AbstractWe 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
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Bibliographic InfoArticle provided by Springer in its journal Metrika.
Volume (Year): 75 (2012)
Issue (Month): 6 (August)
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Web page: http://www.springerlink.com/link.asp?id=102509
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