• The Korean Journal of Applied Statistics
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• v.16 no.2
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• pp.273-282
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• 2003

The problem of estimating the parameters of k-population Weibull distributions is discussed under the prior of ordered scale parameters. Parameters are estimated by the Gibbs sampling method. Since the conditional posterior distribution of the shape parameter in the Gibbs sampler is not log-concave, the shape parameter is generated by the adaptive rejection sampling. Finally, we applied this estimation methodology to the data discussed in Nelson (1970).

• Communications for Statistical Applications and Methods
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• v.22 no.2
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• pp.105-120
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• 2015

A large family of distributions arising from distributions of ordered data is proposed which contains other models studied in the literature. This extension subsume many cases of weighted random variables such as order statistics, records, k-records and many others in variety. Such a distribution can be used for modeling data which are not identical in distribution. Some properties of the theoretical model such as moment, mean deviation, entropy criteria, symmetry and unimodality are derived. The proposed model also studies the problem of parameter estimation and derives maximum likelihood estimators in a weighted gamma distribution. Finally, it will be shown that the proposed model is the best among the previously introduced distributions for modeling a real data set.

• Water for future
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• v.20 no.2
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• pp.117-126
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• 1987

A Synthetic unit hydrograph method was suggested for the representation of a direct runoff hydrograph with empirical geomorphologic laws and geomorphologic parameters by applying geomorphologic instantaneous unit hydrograph theory and Rossois results of application of GIUH theory to the Nash Model which is a linear reservoir model. The shape parameter m and scale parameter k can be derived by the Horton's empirical geomorphologic laws $R_A,R_B,R_L$ when ordered according to Strahler's ordering Scheme, main stream length and using the maximum velocity for the dynamic characteristics of a river basin, The derived response function was tested on some observed flood datas and showed promising. For the determination of the shape parameter m, eq. (16) was showed applying and m showed a good regression with the size of basin area.

• Journal of Korea Water Resources Association
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• v.32 no.5
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• pp.565-577
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• 1999

The geometric patterns of a stream network in a drainage basin can be viewed as a "fractal" with fractal dimensions. Fractals provide a mathematical framework for treatment of irregular, ostensively complex shapes that show similar patterns or geometric characteristics over a range of scale. GIUH (Geomorphological Instantaneous Unit Hydrograph) is based on the hydrologic response of surface runoff in a catchment basin. This model incorporates geomorphologic parameters of a basin using Horton's order ratios. For an ordered drainage system, the fractal dimensions can be derived from Horton's laws of stream numbers, stream lengths and stream areas. In this paper, a fractal approach, which is leading to representation of a 2-parameter Gamma distribution type GIUH, has been carried out to incorporate the self similarity of the channel networks based on the high correlations between the Horton's order ratios. The shape and scale parameter of the GIUH-Nash model of IUH in terms of Horton's order ratios of a catchment proposed by Rosso(l984J are simplified by applying the fractal dimension of main stream length and channel network of a river basin. basin.