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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.

MSC:

62G10 Nonparametric hypothesis testing
62G20 Asymptotic properties of nonparametric inference
62F12 Asymptotic properties of parametric estimators
62G32 Statistics of extreme values; tail inference
62G05 Nonparametric estimation
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