• Title, Summary, Keyword: weighted distribution

### Variable Sampling Interval $\bar{X}$ Control Chart Using Weighted Standard Deviation Method (가중표준편차를 이용한 가변표본채취간격 $\bar{X}$ 관리도)

• Chang, Youngsoon
• 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.

### CLOSURE PROPERTY AND TAIL PROBABILITY ASYMPTOTICS FOR RANDOMLY WEIGHTED SUMS OF DEPENDENT RANDOM VARIABLES WITH HEAVY TAILS

• Dindiene, Lina;Leipus, Remigijus;Siaulys, Jonas
• 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.

### Better Estimators of Multiple Poisson Parameters under Weighted Loss Function

• Kim, Jai-Young
• Journal of the military operations research society of Korea
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• v.11 no.2
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• pp.69-82
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• 1985
• In this study, we consider the simultaneous estimation of the parameters of the distribution of p independent Poisson random variables using the weighted loss function. The relation between the estimation under the weighted loss function and the case when more than one observation is taken from some population is studied. We derive an estimator which dominates Tsui and Press's estimator when certain conditions hold. We also derive an estimator which dominates the maximum likelihood estimator(MLE) under the various loss function. The risk performances of proposed estimators are compared to that of MLE by computer simulation.

### WEIGHTED COMPOSITION OPERATORS ON LORENTZ SPACES

• Arora, Subhash Chander;Datt, Gopal;Verma, Satish
• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.701-708
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• 2007
• In this paper we characterize the boundedness, compactness and closedness of the range of the weighted composition operators on Lorentz spaces L(p,q), \$1.

### A Success factor for Technology Commercialization for Start-ups by the Weighted-BMO Model (BMO모형을 이용한 스타트업 기술사업화 성공요인 연구)

• Min, Kwang-Dong;Huh, Moo-Yul;Han, Jeong-Hui
• 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.

### Generalized Weighted Linear Models Based on Distribution Functions - A Frequentist Perspective (분포함수를 기초로 일반화가중선형모형)

• 여인권
• 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.

### A Bayesian Approach to Fuzzy Hypotheses Testing with Revision of possibility distribution

• 강만기
• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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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.

### Development of Weigh Calculation Method for Pavement Roughness Index Considering Vehicle Wandering Distribution (원더링 분포를 고려한 도로포장 평탄성 지수의 가중치 산정기법 개발)

• Lee, Jaehoon;Sohn, Ducksu;Park, Jejin;Cho, Yoonho
• International Journal of Highway Engineering
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• v.19 no.5
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• pp.89-96
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• 2017
• PURPOSES: This study aims to develop a rational procedure for estimating the pavement roughness index considering vehicle wandering. METHODS : The location analysis of the passing vehicle in the lane was performed by approximately 1.2 million vehicles for verification of the wandering distribution. According to verification result, the distribution follows the normal distribution pattern. The probability density function was estimated using each lane's wandering distribution model. Then the procedure for applying a weighted value into the lane profile was conducted using this function. RESULTS : The modified index, MRIw, with consideration towards applying the wandering weighted value application was computed then compared with MRI. It was found that the Coefficient of Variation for distribution of lateral roughness index in the lane was high in the case of a large difference between each index (i.e., MRIw and MRI) observed. CONCLUSIONS : This result confirms that the new procedure with consideration of the weight factor can successfully improve the lane representative characteristics of the roughness index.

### Temperature distribution analysis of steel box-girder based on long-term monitoring data

• Wang, Hao;Zhu, Qingxin;Zou, Zhongqin;Xing, Chenxi;Feng, Dongming;Tao, Tianyou
• Smart Structures and Systems
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• v.25 no.5
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• pp.593-604
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• 2020
• Temperature may have more significant influences on structural responses than operational loads or structural damage. Therefore, a comprehensive understanding of temperature distributions has great significance for proper design and maintenance of bridges. In this study, the temperature distribution of the steel box girder is systematically investigated based on the structural health monitoring system (SHMS) of the Sutong Cable-stayed Bridge. Specifically, the characteristics of the temperature and temperature difference between different measurement points are studied based on field temperature measurements. Accordingly, the probability density distributions of the temperature and temperature difference are calculated statistically, which are further described by the general formulas. The results indicate that: (1) the temperature and temperature difference exhibit distinct seasonal characteristics and strong periodicity, and the temperature and temperature difference among different measurement points are strongly correlated, respectively; (2) the probability density of the temperature difference distribution presents strong non-Gaussian characteristics; (3) the probability density function of temperature can be described by the weighted sum of four Normal distributions. Meanwhile, the temperature difference can be described by the weighted sum of Weibull distribution and Normal distribution.

### Improvements in Speaker Adaptation Using Weighted Training (가중 훈련을 이용한 화자 적응 시스템의 향상)

• 장규철;우수영;진민호;박용규;유창동
• The Journal of the Acoustical Society of Korea
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• v.22 no.3
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• pp.188-193
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• 2003
• Regardless of the distribution of the adaptation data in the testing environment, model-based adaptation methods that have so far been reported in various literature incorporates the adaptation data undiscriminatingly in reducing the mismatch between the training and testing environments. When the amount of data is small and the parameter tying is extensive, adaptation based on outlier data can be detrimental to the performance of the recognizer. The distribution of the adaptation data plays a critical role on the adaptation performance. In order to maximally improve the recognition rate in the testing environment using only a small number of adaptation data, supervised weighted training is applied to the structural maximum a posterior (SMAP) algorithm. We evaluate the performance of the proposed weighted SMAP (WSMAP) and SMAP on TIDIGITS corpus. The proposed WSMAP has been found to perform better for a small amount of data. The general idea of incorporating the distribution of the adaptation data is applicable to other adaptation algorithms.