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A test procedure for detecting super-heavy tails. (English) Zbl 1149.62036
Summary: The aim of this work is to develop a test to distinguish between heavy and super-heavy tailed probability distributions. These classes of distributions are relevant in areas such as telecommunications and insurance risk, among others. By heavy tailed distributions we mean probability distribution functions with polynomially decreasing upper tails (regularly varying tails). The term super-heavy is reserved for right tails decreasing to zero at a slower rate, such as logarithmic, or worse (slowly varying tails). Simulations are presented for several models and an application with telecommunications data is provided.
62G10Nonparametric hypothesis testing
62G20Nonparametric asymptotic efficiency
62F12Asymptotic properties of parametric estimators
62G32Statistics of extreme values; tail inference
62G05Nonparametric estimation
[1]Adler, R.; Feldman, R.; Taqqu, M. S.: Practical guide to heavy tails: statistical techniques for analyzing heavy tailed distributions, (1998) · Zbl 0901.00010
[2]Bettini, C., 1987. Forecasting populations of undiscovered oil fields with the log-Pareto distribution. Ph.D. Thesis, Stanford University, SU, USA.
[3]Billingsley, P.: Weak convergence of measures: applications in probability, (1971) · Zbl 0271.60009
[4]Bingham, N. H.; Goldie, C. M.; Teugels, J. L.: Regular variation, Encyclopedia of mathematics and its application 27 (1987)
[5]Crovella, M., Lipsky, L., 1997. Long-lasting transient conditions in simulations with heavy-tailed workloads. In: Andradóttir, S., Healy, K., Whithers, D., Nelson, B. (Eds.), Winter Simulation Conference.
[6]Csörgő, M.; Horváth, L.: Weighted approximations in probability and statistics, (1993) · Zbl 0770.60038
[7]De Alba, E.; Mendoza, M.: Forecasting an accumulated series based on partial accumulation: a Bayesian method for short series with seasonal patterns, J. business econ. Statist. 19, 95-102 (2001)
[8]De Haan, L.; Ferreira, A.: Extreme value theory: an introduction. Springer series in operations research and financial engineering, (2006)
[9]De Haan, L.; Rootzén, H.: On the estimation of high quantiles, J. statist. Plann. inference 35, 1-13 (1993) · Zbl 0770.62026 · doi:10.1016/0378-3758(93)90063-C
[10]De Haan, L.; Stadtmüller, U.: Generalized regular variation of second order, J. austral. Math. soc. 61(A), 381-395 (1996) · Zbl 0878.26002
[11]Desgagné, A.; Angers, J. -F.: Importance sampling with the generalized exponential power density, Statist. comput. 15, 189-196 (2005)
[12]Diebolt, J.; El-Aroui, M.; Garrido, M.; Girard, S.: Quasi-conjugate Bayes estimates for GPD parameters and application to heavy tails modeling, Extremes 8, 57-78 (2005) · Zbl 1091.62009 · doi:10.1007/s10687-005-4860-9
[13]Drees, H.: On smooth statistical tail functionals, Scand. J. Statist. 25, 187-210 (1998) · Zbl 0923.62032 · doi:10.1111/1467-9469.00097
[14]Heffernan, J., Resnick, S., 2007. Limit laws for random vectors with an extreme component. Ann. Appl. Probab. 17, 537 – 571. · Zbl 1125.60049 · doi:10.1214/105051606000000835
[15]Jung, J.; Sit, E.; Balakrishnan, H.; Morris, R.: DNS performance and the effectiveness of caching, IEEE/ACM trans. Networking 10, 589-603 (2002)
[16]Jung, J., Berger, A., Balakrishnan, H., 2003. Modeling TTL-based internet caches. In: Proceedings of the IEEE Infocom, San Francisco, CA.
[17]Mikosch, T.; Resnick, S.: Activity rates with very heavy tails, Stoch. processes appl. 116, No. 2, 131-155 (2006) · Zbl 1090.60075 · doi:10.1016/j.spa.2005.08.003
[18]Neves, C.; Alves, M. Fraga: The ratio of maximum to the sum for testing super heavy tails, Advances in mathematical and statistical modeling (2008)
[19]Resnick, S.: Point processes, regular variation and weak convergences, Adv. appl. Probab. 18, No. 1, 66-138 (1986) · Zbl 0597.60048 · doi:10.2307/1427239
[20]Smirnov, N. V.: Limit distributions for the terms of a variational series, Amer. math. Soc. transl. Ser. I 1, No. 67, 82-143 (1952)
[21]Tsourti, Z.; Panaretos, J.: Extreme-value analysis of teletraffic datas, Comput. statist. Data anal. 45, 85-103 (2004)
[22]Zeevi, A.; Glynn, P.: Recurrence properties of autoregressive processes with super-heavy tailed innovations, J. appl. Probab. 41, No. 3, 639-653 (2004) · Zbl 1115.62092 · doi:10.1239/jap/1091543415 · doi:euclid:jap/1091543415