Title: The Greenwood statistic, stochastic dominance, clustering and heavy tails
Authors: Anna Panorska - University of Nevada (United States) [presenting]
Tomasz Kozubowski - University of Nevada Reno (United States)
Marek Arendarczyk - University of Wroclaw (Poland)
Abstract: The Greenwood statistic $T_n$ and its functions, including sample coefficient of variation, often arise in testing exponentiality or detecting clustering or heterogeneity. We provide a general result describing the stochastic behavior of $T_n$ in response to stochastic behavior of the sample data. Our result provides a rigorous base for constructing tests and assuring that confidence regions are actually intervals for the tail parameter of many power-tail distributions. We also present a result explaining the connection between clustering and heaviness of tail for several standard classes of distributions and argue its extension to general heavy-tailed families. The results provide theoretical justification for $T_n$ being an effective and commonly used statistic discriminating between regularity/uniformity and clustering in the presence of heavy tails in applied sciences. We also note that the use of Greenwood statistic as a measure of heterogeneity or clustering is limited to data with large outliers, as opposed to those close to zero.