• Journal of the Korean Mathematical Society
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• v.58 no.3
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• pp.741-760
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• 2021

In this paper, we exhibit the equivalence between different notions of unique range sets, namely, unique range sets, weighted unique range sets and weak-weighted unique range sets under certain conditions. Also, we present some uniqueness theorems which show how two meromorphic functions are uniquely determined by their two finite shared sets. Moreover, in the last section, we make some observations that help us to construct other new classes of unique range sets.

• The Journal of Industrial Distribution & Business
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• v.8 no.6
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• pp.87-95
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• 2017

Purpose - The structural changes of Korean agriculture are complex due to heterogeneous production processes and farms' features. This study analyzed trends of dualism in Korean agriculture over the period 2000-15 based on farm-level data to clarify the specific trends of dualism in terms of farm income, farm-size, and farm operators' age. From the results of this study, we would be able to understand the features of structural changes in Korean agriculture more profoundly. Research design, data, and methodology - We incorporated farm-level data in South Korea: Agricultural census and Farm household economy survey. As measures of inequality, we used size-weighted quantiles, and normalized Gini coefficients as well as mean and conventional quantiles. The size-weighted quantiles are more robust to changes in the number of small farms, but they are more sensitive to changes in the distribution of farm-size. Thus, they would be more useful to identify trends of dualism of Korean agriculture. Results - The results show that the farmland distribution of crop farms became more skewed and dispersed. However, the herd distribution of livestock farms became more concentrated. To be specific, their mean and 1st quantile increases more rapidly than their size-weighted 2nd quantile and size-weighted 3rd quantile. Gini coefficients of livestock farms regarding their herd distribution decreased by 0.1 on average. In the case of income distribution, the results indicate that the polarization regarding farm household/agricultural/non-agricultural income became more severe. However, we also found that the distribution of transfer income became concentrated continuously. The results imply that transfer income including subsidies would decrease farm income polarization. Lastly, during the study periods, Korean farms were aging over time, and age distribution of them more concentrated. Conclusions - The structure of Korean agriculture has been changing, even though the absolute size of it decreased over time. Land (herd) distribution became more dispersed (concentrated). Inequality regarding agricultural income became more severe, and it made farm household income more polarized even though transfer income would decrease income gaps among farms. Lastly, farms continue to age regardless of farm types and this might affect the structural changes in Korean agriculture in the future.

• Journal of the Korean Operations Research and Management Science Society
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• v.39 no.1
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• pp.1-12
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• 2014

This article proposes a variable sampling interval (VSI) $\bar{X}$ control chart using weighted standard deviation (WSD) method for skewed populations. The WSD method decomposes the standard deviation of a quality characteristic into upper and lower deviations and adjusts control limits and warning limits of a control chart in accordance with the direction and degree of skewness. A control chart constant is derived for estimating the standard deviation of skewed distributions with the mean of sample standard deviations. The proposed chart is compared with the conventional VSI $\bar{X}$ control chart under some skewed distributions. Simulation study shows that the proposed WSD VSI chart can control the in-control average time to signal (ATS) as an adequate level better than the conventional VSI chart, and the proposed chart can detect a decrease in the process mean of a quality characteristic following a positively skewed distribution more quickly than the standard VSI chart.

• Proceedings of the Korean Society of Agricultural Engineers Conference
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• 2003.10a
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• pp.511-514
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• 2003

This study was conducted to estimate the design rainfall by the determination of best fitting order for Higher Probability Weighted Moments of the annual maximum series according to consecutive duration at sixty-five rainfall stations in Korea. Design rainfalls were obtained by generalized extreme value distribution which was selected to be suitable distribution in 4 applied distributions and by L, L1, L2, L3 and L4-moment. The best fitting order for Higher Probability Weighted Moments was determined with the confidence analysis of estimated design rainfall.

• Journal of the Korean Mathematical Society
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• v.54 no.6
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• pp.1879-1903
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• 2017

In this paper we study the closure property and probability tail asymptotics for randomly weighted sums $S^{\Theta}_n={\Theta}_1X_1+{\cdots}+{\Theta}_nX_n$ for long-tailed random variables $X_1,{\ldots},X_n$ and positive bounded random weights ${\Theta}_1,{\ldots},{\Theta}_n$ under similar dependence structure as in [26]. In particular, we study the case where the distribution of random vector ($X_1,{\ldots},X_n$) is generated by an absolutely continuous copula.

• Communications for Statistical Applications and Methods
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• v.9 no.2
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• pp.305-313
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• 2002

Regarding to inference about a scalar measure of internal scatter of Ρ-variate normal population, this paper considers an interval estimation of the generalized variance, │$\Sigma$│. Due to complicate sampling distribution, fully parametric frequentist approach for the interval estimation is not available and thus Bayesian method is pursued to calculate the highest probability density (HPD) interval for the generalized variance. It is seen that the marginal posterior distribution of the generalized variance is intractable, and hence a weighted Monte Carlo method, a variant of Chen and Shao (1999) method, is developed to calculate the HPD interval of the generalized variance. Necessary theories involved in the method and computation are provided. Finally, a simulation study is given to illustrate and examine the proposed method.

• The Journal of Industrial Distribution & Business
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• v.9 no.11
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• pp.39-54
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• 2018

Purpose - To success, in spite of deficient resources, a start-up company has to check various circumstances. Many researchers proposed different appraisal methods for technology commercialization. But everybody agrees Merrifield is the first one, who is a pioneer of an appraisal model of technology commercialization. After he proposed it, many researchers and field workers developed a more complicated model, which called a BMO model. In this research, considering the circumstances of start-ups that lack available resources, it proposes a new appraisal method for technology commercialization, which is named a weighted-BMO model. Research design, data, and methology - For the new BMO-model, it studied the preceding studies. And it found that the success factors for start-ups were correlated with technology commercialization. After comparing the success factors for technology commercialization of start-ups with BMO appraisal factor, it withdraws the net BMO appraisal model: which we are calling the weighted-BMO model. Results - This study found a few things. First, actually, the BMO appraisal factors related with the success factors of technology commercialization. Second, the weighted-BMO model, which included the entrepreneur ability factor, was more accurately estimated the success of technology-based start-ups than the BMO model. Third, it overcame the weakness of the BMO-model, which did not include quantitative factors. In addition to evaluating the feasibility of the BMO model, we also presented a strategy for the future direction. But, still, it included a few shortcomings, which we are calling the arbitrage of weighted value. Sometimes, the intentional weighted value can deliberate the different valuation. Conclusitons - Due to this study, the weighted-BMO model included appraisal factors related with the success factors of technology commercialization and the entrepreneur ability factor, and quantitative factors. When evaluating the combined score of the existing Merrified BMO components, 35 points of the first pass criterion accounted for 29.17% of the total score, and 80 points of the merit score of the second rank criterion were 66.67% Considering that the weighted sum is taken into account, the baseline score of the weighted summing method for each component of the modified BMO model is 2.92 points, which is 29.17% of the weighted sum total of 10 points. The evaluation score was 6.67 points, 66.67% of the weighted total score of 10 points.

• The Korean Journal of Applied Statistics
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• v.17 no.3
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• pp.489-498
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• 2004

In this paper, a new form of linear models referred to as generalized weighted linear models is proposed. The proposed models assume that the relationship between the response variable and explanatory variables can be modelled by a distribution function of the response mean and a weighted linear combination of distribution functions of covariates. This form addresses a structural problem of the link function in the generalized linear models in which the parameter space may not be consistent with the space derived from linear predictors. The maximum likelihood estimation with Lagrange's undetermined multipliers is used to estimate the parameters and resampling method is applied to compute confidence intervals and to test hypotheses.

• Communications for Statistical Applications and Methods
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• v.14 no.3
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• pp.561-576
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• 2007

Five plotting positions are applied to the computation of probability weighted moments (PWM) on the parameters of the generalized logistic distribution. Over a range of parameter values with some finite sample sizes, the effects of five plotting positions are investigated via Monte Carlo simulation studies. Our simulation results indicate that the Landwehr plotting position frequently tends to document smaller biases than others in the location and scale parameter estimations. On the other hand, the Weibull plotting position often tends to cause larger biases than others. The plotting position (i - 0.35)/n seems to report smaller root mean square errors (RMSE) than other plotting positions in the negative shape parameter estimation under small samples. In comparison to the maximum likelihood (ML) method under the small sample, the PWM do not seem to be better than the ML estimators in the location and scale parameter estimations documenting larger RMSE. However, the PWM outperform the ML estimators in the shape parameter estimation when its magnitude is near zero. Sensitivity of right tail quantile estimation regarding five plotting positions is also examined, but superiority or inferiority of any plotting position is not observed.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.13.2-13
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• 2003

We propose some properties of Bayesian fuzzy hypotheses testing by revision for prior possibility distribution and posterior possibility distribution using weighted fuzzy hypotheses versus on with loss function.