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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:
62G10Nonparametric hypothesis testing
62G20Nonparametric asymptotic efficiency
62F12Asymptotic properties of parametric estimators
62G32Statistics of extreme values; tail inference
62G05Nonparametric estimation
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