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**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 |

### Keywords:

maximum likelihood estimation; method of moments estimation; L-moments; simulation; flood frequency analysis
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\textit{Md. S. Murshed} et al., Stoch. Environ. Res. Risk Assess. 25, No. 7, 897--911 (2011; Zbl 1221.62027)

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