• Proceedings of the Korea Water Resources Association Conference
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• 2004.05b
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• pp.595-598
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• 2004

This research seeks to derive the design rainfalls through the L-moment with the test of homogeneity, independence and outlier of data on annual maximum daily rainfall at 38 rainfall stations in Korea. To select the appropriate distribution of annual maximum daily rainfall data by the rainfall stations, Generalized Extreme Value (GEV), Generalized Logistic (GLO), Generalized Pareto (GPA), Generalized Normal (GNO) and Pearson Type 3 (PT3) probability distributions were applied and their aptness were judged using an L-moment ratio diagram and the Kolmogorov-Smirnov (K-S) test. Parameters of appropriate distributions were estimated from the observed and simulated annual maximum daily rainfall using Monte Carlo techniques. Design rainfalls were finally derived by GEV distribution, which was proved to be more appropriate than the other distributions.

• Journal of The Korean Society of Agricultural Engineers
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• v.46 no.3
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• pp.31-42
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• 2004

This research seeks to derive the design rainfalls through the L-moment with the test of homogeneity, independence and outlier of data on annual maximum daily rainfall at 38 rainfall stations in Korea. To select the appropriate distribution of annual maximum daily rainfall data by the rainfall stations, Generalized Extreme Value (GEV), Generalized Logistic (GLO), Generalized Pareto (GPA), Generalized Normal (GNO) and Pearson Type 3 (PT3) probability distributions were applied and their aptness were judged using an L-moment ratio diagram and the Kolmogorov-Smirnov (K-S) test. Parameters of appropriate distributions were estimated from the observed and simulated annual maximum daily rainfall using Monte Carlo techniques. Design rainfalls were finally derived by GEV distribution, which was proved to be more appropriate than the other distributions.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.325-332
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• 2009

Reducing the generalized logarithmic functional equations to differential equations in the sense of Schwartz distributions, we find the locally integrable solutions of the equations.

• Journal of the Korean Statistical Society
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• v.34 no.4
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• pp.311-329
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• 2005

Skewed t distributions have attracted significant attention in the last few years. In this paper, a generalization - referred to as the skewed generalized t distribution - with the pdf f(x) = 2g(x)G(${\lambda}x$) is introduced, where g(${\cdot}$) and G (${\cdot}$) are taken, respectively, to be the pdf and the cdf of the generalized t distribution due to McDonald and Newey (1984, 1988). Several particular cases of this distribution are identified and various representations for its moments derived. An application is provided to rainfall data from Orlando, Florida.

• Journal of The Korean Society of Agricultural Engineers
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• v.51 no.3
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• pp.53-62
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• 2009

This study was carried out to select optimal probability distribution based on design accumulated monthly mean inflow from the viewpoint of drought by Gamma (GAM), Generalized extreme value (GEV), Generalized logistic (GLO), Generalized normal (GNO), Generalized pareto (GPA), Gumbel (GUM), Normal (NOR), Pearson type 3 (PT3), Wakeby (WAK) and Kappa (KAP) distributions for the observed accumulative monthly mean inflow of Chungjudam. L-moment ratio was calculated using observed accumulative monthly mean inflow. Parameters of 10 probability distributions were estimated by the method of L-moments with the observed accumulated monthly mean inflow. Design accumulated monthly mean inflows obtained by the method of L-moments using different methods for plotting positions formulas in the 10 probability distributions were compared by relative mean error (RME) and relative absolute error (RAE) respectively. It has shown that the design accumulative monthly mean inflow derived by the method of L-moments using Weibull plotting position formula in WAK and KAP distributions were much closer to those of the observed accumulative monthly mean inflow in comparison with those obtained by the method of L-moment with the different formulas for plotting positions in other distributions from the viewpoint of RME and RAE.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.517-530
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• 2015

In this paper, we establish a class of strong limit theorems, represented by inequalities, for the arbitrary random field with respect to the product binomial distributions indexed by the infinite tree on the generalized random selection system by constructing the consistent distri-bution and a nonnegative martingale with pure analytical methods. As corollaries, some limit properties for the Markov chain field with respect to the binomial distributions indexed by the infinite tree on the generalized random selection system are studied.

• Asian Pacific Journal of Cancer Prevention
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• v.13 no.5
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• pp.1829-1831
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• 2012

Background: The generalized gamma distribution statistics constitute an extensive family that contains nearly all of the most commonly used distributions including the exponential, Weibull and log normal. A saturated version of the model allows covariates having effects through all the parameters of survival time distribution. Accelerated failure-time models assume that only one parameter of the distribution depends on the covariates. Methods: We fitted both the conventional GG model and the saturated form for each of its members including the Weibull and lognormal distribution; and compared them using likelihood ratios. To compare the selected parameter distribution with log logistic distribution which is a famous distribution in survival analysis that is not included in generalized gamma family, we used the Akaike information criterion (AIC; r=l(b)-2p). All models were fitted using data for 369 women age 50 years or more, diagnosed with stage IV breast cancer in BC during 1990-1999 and followed to 2010. Results: In both conventional and saturated parametric models, the lognormal was the best candidate among the GG family members; also, the lognormal fitted better than log-logistic distribution. By the conventional GG model, the variables "surgery", "radiotherapy", "hormone therapy", "erposneg" and interaction between "hormone therapy" and "erposneg" are significant. In the AFT model, we estimated the relative time for these variables. By the saturated GG model, similar significant variables are selected. Estimating the relative times in different percentiles of extended model illustrate the pattern in which the relative survival time change during the time. Conclusions: The advantage of using the generalized gamma distribution is that it facilitates estimating a model with improved fit over the standard Weibull or lognormal distributions. Alternatively, the generalized F family of distributions might be considered, of which the generalized gamma distribution is a member and also includes the commonly used log-logistic distribution.

• 한국데이터정보과학회:학술대회논문집
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• 2005.10a
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• pp.27-34
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• 2005

We consider the problem of estimating the system reliability noninformative priors when both stress and strength follow generalized gamma distributions. We first derive Jeffreys' prior, group ordering reference priors, and matching priors. We investigate the propriety of posterior distributions and provide marginal posterior distributions under those noninformative priors. We also examine whether the reference priors satisfy the probability matching criterion.

• Journal of Applied Reliability
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• v.11 no.2
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• pp.151-165
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• 2011

We consider the problem of estimating the system reliability using noninformative priors when both stress and strength follow generalized gamma distributions with index, scale, and shape parameters. We first derive group-ordering reference priors using the reparametrization. We next provide the sufficient condition for propriety of posterior distributions and provide marginal posterior distributions under those noninformative priors. Finally, we provide and compare estimated values of the system reliability based on the simulated values of parameter of interest in some special cases.

• Journal of applied mathematics & informatics
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• v.41 no.4
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• pp.821-829
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• 2023

In this paper, we obtain characterizations of continuous distributions based on the independent property of generalized record values extending the characterization results reported by Jin and Lee [4], Skřivánková and Juhás [8]. Also, example of special cases of general classes as Bur types, Pareto, power and Weibull distribution are discussed.