Abstract
A description of the mathematical properties of three-parameter kappa distribution (K3D) is provided. We consider the hazard rate function, the rth moment, the rth L-moment, and the asymptotic distribution of the extreme order statistics and their graphical illustrations. It turns out that this distribution is close to a generalized Pareto distribution, so that the K3D is suitable for modeling threshold excesses or modeling data that has a lower bound. In addition we studied three estimation methods (method of moments, method of L-moments, and maximum likelihood). The Monte Carlo simulation for performance evaluation shows that the maximum likelihood estimator and the L-moment estimator worked equally well. The method of moments estimator worked poorly for all cases. We illustrate its applicability for daily rainfall data.
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