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A three-parameter kappa distribution with hydrologic application: a generalized gumbel distribution

Authors
  • Jeong, Bo Yoon
  • Murshed, Md. Sharwar
  • Seo, Yun Am
  • Park, Jeong-Soo
Type
Published Article
Journal
Stochastic Environmental Research and Risk Assessment
Publisher
Springer-Verlag
Publication Date
Mar 26, 2014
Volume
28
Issue
8
Pages
2063–2074
Identifiers
DOI: 10.1007/s00477-014-0865-8
Source
Springer Nature
Keywords
License
Yellow

Abstract

A three-parameter kappa distribution (K3D) as a special case of the four-parameter kappa distribution is studied. This distribution (K3D) is viewed as a generalized Gumbel distribution. A description of the mathematical properties of K3D is provided. We consider the moment generating function, the moments, the L-moments, LH-moments, the asymptotic distribution of the extreme order statistics, and its graphical illustrations. Parameters are estimated by using the method of L-moments and maximum likelihood method. A Monte-Carlo simulation study is given to compare the estimation methods. To illustrate its applicability, heavy rainfall data from Korea is analyzed, and the fitness is compared with Gumbel, generalized extreme value and four-parameter kappa distributions.

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