Abstract
In many practical situations exploratory plots are helpful in understanding tail behavior of sample data. The Mean Excess plot is one of the exploratory tools often used in practice to understand the right tail behavior of a data set. It is known that if the underlying distribution of a data sample is in the maximum domain of attraction of a Fréchet, a Gumbel or a Weibull distributions then the ME plot of the data approaches a straight line in an appropriate sense, with positive, zero or negative slope respectively. In this paper we construct confidence intervals around the ME plots which assist us in ascertaining which particular maximum domain of attraction the data set comes from. We recall weak limit results for the Fréchet domain of attraction, already obtained in Das and Ghosh (Bernoulli 19, 308–342 2013) and derive weak limits for the Gumbel and Weibull domains in order to construct confidence bounds. We demonstrate our methodology by applying them to simulated and real data sets.
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Bikramjit Das gratefully acknowledges support from SRG ESD 047 and MIT-SUTD IDC grant IDG31300110. The authors are grateful to the anonymous referees for their valuable comments which have helped improve the article.
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Das, B., Ghosh, S. Detecting tail behavior: mean excess plots with confidence bounds. Extremes 19, 325–349 (2016). https://doi.org/10.1007/s10687-015-0238-9
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DOI: https://doi.org/10.1007/s10687-015-0238-9