Akademik Veri Yönetim Sistemi
15th International Conference on Ordered Statistical Data, Coimbra, Portekiz, 11 - 14 Haziran 2024, ss.46
The four-parameter kappa distribution, as defined by Hosking [1], includes four distinct extreme value models and has extensive applications in various fields such as environmental sciences and hydrology. As a special case, the three-parameter kappa distribution, also referred to as K3D, is previously overlooked in the literature until Jeong [2] undertook a comprehensive study on it. In this talk, we consider the K3D for order statistics point of view and obtain moments of order statistics from it. Moreover, we derive some useful recurrence relations for calculating both single and product moments of order statistics. As an application of these relations, we use these calculations to derive the best linear unbiased estimator (BLUE) for estimating the location and scale parameters of the distribution. Finally, we demonstrate a representative data fitting to see the performance of the BLUE’s versus the maximum likelihood estimates.
References
[1] Hosking, J. R. (1994). The four-parameter kappa distribution. IBM Journal of Research and Development 38, 251—258.
[2] Jeong, B.Y., Murshed, M. S., Seo, Y.A., Park, J.S. (2014). A three-parameter kappa distribution with hydrologic application: a generalized Gumbel distribution. Stochastic Environmental Research and Risk Assessment 28, 2063–2074.