## 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.

### MSC:

 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

### Software:

lmoments; LMOMENTS; Mathematica; ismev
Full Text:

### References:

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