A Methodology for Characterising the Tail Behaviour of a Distribution
Following a review of various approaches that are utilized for classifying the tail behavior of a distribution, an easily implementable methodology that relies on an arctangent transformation is presented. The classification criterion is actually based on the difference between two specific quantiles of the transformed distribution. The resulting categories enable one to classify distributional tails as distinctly short, short, nearly medium, medium, extended medium and somewhat long, providing that at least two moments exist. Distributions possessing a single moment are said to be long tailed while those failing to have any finite moments are classified as having an extremely long tail. Several illustrative examples will be presented.
 S. A. Klugman, H. H. Panjer, and G. E. Willmot, “Loss Models: from Data to Decisions, 4th Ed.” John Wiley & Sons, New York, 2012.
 E. Parzen, “Nonparametric statistical data modeling,” Journal of the American Statistical Association, vol. 74, pp. 105-121, 1979.
 E. F. Schuster, “Classification of probability laws by tail behavior,” Journal of the American Statistical Association, vol. 79, pp. 936-939, 1984.
 J. Rojo, “On tail categorization of probability laws,” Journal of the American Statistical Association, vol. 91, pp. 378-384, 1996.
 J. Rojo and R. C. Ott, “Testing for tail behavior using extreme spacings,” arXiv:1011.6458, 2010.
 C. C. Heyde and S. G. Kou,”On the controversy over tailweight of distributions,” Operations Research Letters, vol. 32, pp. 399–408, 2004.
 W.-Y. Loh. “Bounds on are’s for restricted classes of distributions deﬁned vai tail-orderings,” Annals of Statistics, vol.12, pp. 685–701, 1984.
 K. Doksum,.”Starshaped transformations and the power of rank tests,” The Annals of Mathematical Statistics, vol.40, pp.1167–1176, 1969.
 E. Lehmann, “Comparing location experiments,” The Annals of Statistics, vol. 16, pp.521–533, 1988.