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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