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Additional extreme distribution for modeling extreme value data. (English) Zbl 1437.62175

Summary: In this article an additional extreme value distribution (AEVD) is introduced by Box-Cox transformation. Both generalized Pareto distribution under power normalization (GPDP) and generalized extreme value distribution under power normalization (GEVP) can be obtained from AEVD as special cases. The AEVD can be applied in a wide variety of application elds especially for modelling extreme data. A system of nonlinear equations is solved numerically to get maximum likelihood estimation (MLE) for the distribution parameters. The proposed distribution is applied for modelling daily maximum air pollution from Barking Dagenham station. Various criteria reveal that AEVD improves the fitting of this data compared with other distributions.

MSC:

62G32 Statistics of extreme values; tail inference
60G70 Extreme value theory; extremal stochastic processes
62P12 Applications of statistics to environmental and related topics
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