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Exploratory data analysis is often used to test the goodness-of-fit of sampleobservations to specific target distributions. A few such graphical tools havebeen extensively used to detect subexponential or heavy-tailed behavior inobserved data. In this paper we discuss asymptotic limit behavior of two suchplotting tools: the quantile-quantile plot and the mean excess plot. The weakconsistency of these plots to fixed limit sets in an appropriate topology of$\mathbb{R}^2$ has been shown in Das and Resnick (Stoch. Models 24 (2008)103-132) and Ghosh and Resnick (Stochastic Process. Appl. 120 (2010)1492-1517). In this paper we find asymptotic distributional limits for theseplots when the underlying distributions have regularly varying right-tails. Asan application we construct confidence bounds around the plots which enable usto statistically test whether the underlying distribution is heavy-tailed ornot.

Weak limits for exploratory plots in the analysis of extremes