Beta-\(\kappa \) distribution and its application to hydrologic events. (English) Zbl 1221.62027

Summary: The beta-\(\kappa \) distribution is a distinct case of the generalized beta distribution of the second kind. In previous studies, beta-\(p\) and beta-\(\kappa \) distributions have played important roles in representing extreme events, and thus, the present paper uses the beta-\(\kappa \) distribution. Further, this paper uses the method of moments and the method of L-moments to estimate the parameters from the beta-\(\kappa \) distribution, and to demonstrate the performance of the proposed model, the paper presents a simulation study using three estimation methods (including the maximum likelihood estimation method) and beta-\(\kappa \) and non beta-\(\kappa \) samples. In addition, this paper evaluates the performance of the beta-\(\kappa \) distribution by employing two widely used extreme value distributions (i.e., the GEV and Gumbel distributions) and two sets of actual data on extreme events.


62E15 Exact distribution theory in statistics
62F10 Point estimation
62G32 Statistics of extreme values; tail inference
86A05 Hydrology, hydrography, oceanography
65C60 Computational problems in statistics (MSC2010)
86A32 Geostatistics
Full Text: DOI


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