• Journal of the Korean Data and Information Science Society
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• v.25 no.3
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• pp.611-622
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• 2014

The inverse Weibull distribution (IWD) is the complementary Weibull distribution and plays an important role in many application areas. In Bayesian analysis, Soland's method can be considered to avoid computational complexities. One limitation of this approach is that parameters of interest are restricted to a finite number of values. This paper introduce nonparametric Bayesian estimator in the context of record statistics values from the exponentiated inverse Weibull distribution (EIWD). In stead of Soland's conjugate piror, stick-breaking prior is considered and the corresponding Bayesian estimators under the squared error loss function (quadratic loss) and LINEX loss function are obtained and compared with other estimators. The results may be of interest especially when only record values are stored.

• Journal of the Korean Society of Safety
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• v.36 no.2
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• pp.32-38
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• 2021

This paper suggests an approach to evaluate the reliability of an intelligent power module with information deficiency of prior distribution and the characteristics of censored data through Bayesian statistics. This approach used a prior distribution of Bayesian statistics using the lifetime information provided by the manufacturer and compared and evaluated diffuse prior (vague prior) distributions. To overcome the computational complexity of Bayesian posterior distribution, it was computed with Gibbs sampling in the Monte Carlo simulation method. As a result, the standard deviation of the prior distribution developed using simple information was smaller than that of the posterior distribution calculated with the diffuse prior. In addition, it showed excellent error characteristics on RMSE compared with the Kaplan-Meier method.

• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.431-450
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• 2023

The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus to make an approximation of a continuous probability distribution by a discrete distribution. It has broad application in signal processing and data compression. In this paper, first we define the uniform distributions on different curves such as a line segment, a circle, and the boundary of an equilateral triangle. Then, we give the exact formulas to determine the optimal sets of n-means and the nth quantization errors for different values of n with respect to the uniform distributions defined on the curves. In each case, we further calculate the quantization dimension and show that it is equal to the dimension of the object; and the quantization coefficient exists as a finite positive number. This supports the well-known result of Bucklew and Wise [2], which says that for a Borel probability measure P with non-vanishing absolutely continuous part the quantization coefficient exists as a finite positive number.

• Journal of Korean Society of Transportation
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• v.35 no.1
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• pp.63-78
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• 2017

The purpose of this study is to determine the optimal aggregation interval to increase the reliability when estimating representative value of individual vehicle travel time collected by DSRC equipment in interrupted traffic flow section in National Highway. For this, we use the bimodal asymmetric distribution data, which is the distribution of the most representative individual vehicle travel time collected in the interrupted traffic flow section, and estimate the MSE(Mean Square Error) according to the variation of the aggregation interval of individual vehicle travel time, and determine the optimal aggregation interval. The estimation equation for the MSE estimation utilizes the maximum estimation error equation of t-distribution that can be used in asymmetric distribution. For the analysis of optimal aggregation interval size, the aggregation interval size of individual vehicle travel time was only 3 minutes or more apart from the aggregation interval size of 1-2 minutes in which the collection of data was normally lost due to the signal stop in the interrupted traffic flow section. The aggregation interval that causes the missing part in the data collection causes another error in the missing data correction process and is excluded. As a result, the optimal aggregation interval for the minimum MSE was 3~5 minutes. Considering both the efficiency of the system operation and the improvement of the reliability of calculation of the travel time, it is effective to operate the basic aggregation interval as 5 minutes as usual and to reduce the aggregation interval to 3 minutes in case of congestion.

• Journal of Korea Water Resources Association
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• v.55 no.spc1
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• pp.1295-1303
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• 2022

As the role of water distribution networks (WDNs) becomes more important, identifying abnormal events (e.g., pipe burst) rapidly and accurately is required. Since existing approaches such as field equipment-based detection methods have several limitations, model-based methods (e.g., machine learning based detection model) that identify abnormal events using hydraulic simulation models have been developed. However, no previous work has examined the impact of data uncertainties on the results. Thus, this study compares the effects of measurement error-induced pressure data uncertainty in WDNs. An artificial neural network (ANN) is used to predict nodal pressures and measurement errors are generated by using cumulative density function inverse sampling method that follows Gaussian distribution. Total of nine conditions (3 input datasets × 3 output datasets) are considered in the ANN model to investigate the impact of measurement error size on the prediction results. The results have shown that higher data uncertainty decreased ANN model's prediction accuracy. Also, the measurement error of output data had more impact on the model performance than input data that for a same measurement error size on the input and output data, the prediction accuracy was 72.25% and 38.61%, respectively. Thus, to increase ANN models prediction performance, reducing the magnitude of measurement errors of the output pressure node is considered to be more important than input node.

• Journal of Environmental Science International
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• v.26 no.9
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• pp.999-1011
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• 2017

In this study, the Chiu-2D velocity-flow rate distribution based on theoretical background of the entropy probability method was applied to actual ADCP measurement data of Gangjung Stream in Jeju from July 2011 to June 2015 to predict the parameter that take part in velocity distribution of the stream. In addition, surface velocity measured by SIV (Surface Image Velocimeter) was applied to the predicted parameter to calculate discharge. Calculated discharge was compared with observed discharge of ADCP observed during the same time to analyze propriety and applicability of depth of water velocity average conversion factor. To check applicability of the predicted stream parameter, surface velocity and discharge were calculated using SIV and compared with velocity and flow based on ADCP. Discharge calculated by applying velocity factor of SIV to the Chiu-2D velocity-flow rate distribution and discharge based on depth of water velocity average conversion factor of 0.85 were $0.7171m^3/sec$ and $0.5758m^3/sec$, respectively. Their error rates compared to average ADCP discharge of $0.6664m^3/sec$ were respectively 7.63% and 13.64%. Discharge based on the Chiu-2D velocity-flow distribution showed lower error rate compared to discharge based on depth of water velocity average conversion factor of 0.85.

• The Korean Journal of Applied Statistics
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• v.16 no.1
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• pp.101-115
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• 2003

Lately there has been much theoretical and applied interest in linear models with non-normal heavy tailed error distributions. Starting Zellner(1976)'s study, many authors have explored the consequences of non-normality and heavy-tailed error distributions. We consider hierarchical models including selection models under a skewed heavy-tailed e..o. distribution proposed originally by Chen, Dey and Shao(1999) and Branco and Dey(2001) with Dirichlet process prior(Ferguson, 1973) in order to use a meta-analysis. A general calss of skewed elliptical distribution is reviewed and developed. Also, we consider the detail computational scheme under skew normal and skew t distribution using MCMC method. Finally, we introduce one example from Johnson(1993)'s real data and apply our proposed methodology.

• The Korean Journal of Applied Statistics
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• v.33 no.1
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• pp.11-23
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• 2020

Sampling design should provide statistics to meet a given accuracy while saving cost and time. However, a large number of non-responses are occurring due to the deterioration of survey circumstances, which significantly reduces the accuracy of the survey results. Non-responses occur for a variety of reasons. Chung and Shin (2017, 2019) and Min and Shin (2018) found that the accuracy of estimation is improved by removing the bias caused by non-response when the response rate is an exponential or linear function of variable of interests. For that case they assumed that the error of the super population model follows normal distribution. In this study, we proposed a non-response bias adjusted estimator in the case where the error of a super population model follows the gamma distribution or the log-normal distribution in a business survey. We confirmed the superiority of the proposed estimator through simulation studies.

• The Journal of the Acoustical Society of Korea
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• v.16 no.2
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• pp.71-79
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• 1997

In this paper, a codeword-dependent distance normalization(CDDN) and an instar-formed fuzzy smoothing of output distribution are proposed for robust estimation of output probabilities in the FVQ(fuzzy vector quantization)-DHMM(discrete hidden Markov model). The FVQ-DHMM is a variant of DHMM in which the state output probability is estimated by the sum oft he product of the output probability and its weighting factor for each codeword on an input vector. As the performance of the FVQ-DHMM is influenced by weighting factor and output distribution from a state, it is required to get a method to get robust estimation of weighting factors and output distribution for each state. From experimental results, the proposed CDDN method has reduced 24% of error rate over the conventional FVQ-DHMM, and also reduced 79% of error rate when the smoothing of output distribution is also applied to the computation of an output probability. These results indicate that the use of CDDN and the fuzzy smoothing of output distribution to the FVQ-DHMM lead to improved recognition, and therefore it may be used as an alternative to the robust estimation of output probabilities for HMMs.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.24 no.6
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• pp.809-817
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• 2020

In the design and development process of Small-Sat power distribution and transmission module, the stability of dynamic resources was evaluated by a deep learning algorithm. The requirements for the stability evaluation consisted of the power distribution function of the power distribution module and demand module to the SAR radar in Small-Sat. To verify the performance of the switching power components constituting the power module PDM, the reliability was verified using a dynamic neural network. The adoption material of deep learning for reliability verification is the power distribution function of the payload to the power supplied from the small satellite main body. Modeling targets for verifying the performance of this function are output voltage (slew rate control), voltage error, and load power characteristics. First, to this end, the Coefficient Structure area was defined by modeling, and PCB modules were fabricated to compare stability and reliability. Second, Levenberg-Marquare based Two-Way NARX neural network Sigmoid Transfer was used as a deep learning algorithm.