• Journal of the Korean Data and Information Science Society
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• v.16 no.1
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• pp.107-114
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• 2005

We shall consider parametric estimations for the scale parameter in the exponential distribution when the parameter is function of a known exposure level, and obtain expectations and variances for their proposed estimators. And we shall compare numerically efficiencies for proposed estimators of the scale parameter in the small sample sizes.

• Proceedings of the Korea Water Resources Association Conference
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• 2018.05a
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• pp.448-448
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• 2018

In this study, the regression models (Load ESTimator and eight-parameter model) were evaluated to estimate instantaneous pollutant loads under various criteria and optimization methods. As shown in the results, LOADEST commonly used in interpolating pollutant loads could not necessarily provide the best results with the automatic selected regression model. It is inferred that the various regression models in LOADEST need to be considered to find the best solution based on the characteristics of watersheds applied. The recently developed eight-parameter model integrated with Genetic Algorithm (GA) and Gradient Descent Method (GDM) were also compared with LOADEST indicating that the eight-parameter model performed better than LOADEST, but it showed different behaviors in calibration and validation. The eight-parameter model with GDM could reproduce the nitrogen loads properly outside of calibration period (validation). Furthermore, the accuracy and precision of model estimations were evaluated using various criteria (e.g., $R^2$ and gradient and constant of linear regression line). The results showed higher precisions with the $R^2$ values closed to 1.0 in LOADEST and better accuracy with the constants (in linear regression line) closed to 0.0 in the eight-parameter model with GDM. In hence, based on these finding we recommend that users need to evaluate the regression models under various criteria and calibration methods to provide the more accurate and precise results for pollutant load estimations.

• Communications for Statistical Applications and Methods
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• v.24 no.1
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• pp.15-27
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• 2017

This paper introduces a two-parameter discrete distribution based on a continuous two-parameter bathtub distribution. It is the only two-parameter discrete distribution that shows a bathtub-shaped hazard function. Some statistical properties of the distribution are discussed. Three different methods are used to estimate its two unknown parameters. The point estimators of the parameters have no closed form. The bootstrap method is used to estimate the distributions of these point estimators. Different approximations of the interval estimations for the two-parameters are discussed. Real data sets are analyzed to show how this distribution works in practice. A simulation study is performed to investigate the properties of the estimations obtained and compare their performances.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.15 no.2
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• pp.123-135
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• 2011

In this paper, we present arc-length estimations for quadratic rational B$\acute{e}$zier curves using the length of polygon and distance between both end points. Our arc-length estimations coincide with the arc-length of the quadratic rational B$\acute{e}$zier curve exactly when the weight ${\omega}$ is 0, 1 and ${\infty}$. We show that for all ${\omega}$ > 0 our estimations are strictly increasing with respect to ${\omega}$. Moreover, we find the parameter ${\mu}^*$ which makes our estimation coincide with the arc-length of the quadratic rational B$\acute{e}$zier curve when it is a circular arc too. We also show that ${\mu}^*$ has a special limit, which is used for optimal estimation. We present some numerical examples, and the numerical results illustrates that the estimation with the limit value of ${\mu}^*$ is an optimal estimation.

• 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.

• Journal of Environmental Science International
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• v.28 no.1
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• pp.19-35
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• 2019

This study investigates the performance of four Bayesian methods, Random Walk Metropolis (RWM), Hit-And-Run Metropolis (HARM), Adaptive Mixture Metropolis (AMM), and Population Monte Carlo (PMC), for estimating the parameters and uncertainties of probability rainfall distribution, and the results are compared with those of conventional parameter estimation methods; namely, the Method Of Moment (MOM), Maximum Likelihood Method (MLM), and Probability Weighted Method (PWM). As a result, Bayesian methods yield similar or slightly better results in parameter estimations compared with conventional methods. In particular, PMC can reduce parameter uncertainty greatly compared with RWM, HARM, and AMM methods although the Bayesian methods produce similar results in parameter estimations. Overall, the Bayesian methods produce better accuracy for scale parameters compared with the conventional methods and this characteristic improves the accuracy of probability rainfall. Therefore, Bayesian methods can be effective tools for estimating the parameters and uncertainties of probability rainfall distribution in hydrological practices, flood risk assessment, and decision-making support.

• Communications for Statistical Applications and Methods
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• v.10 no.1
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• pp.145-151
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• 2003

We shall propose several estimators for the scale parameter in the uniform distribution when the parameter is functions of a known exposure level, and obtain expectations and variances for their proposed estimators. And we shall compare numerically relative efficiencies for proposed estimators of the scale parameter in the small sample sizes.

• International Journal of Contents
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• v.4 no.2
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• pp.19-23
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• 2008

This paper presents a novel method to construct a personalized e-Learning system based on dynamic estimations of item parameters and learners' abilities, where the learning content objects are of the same intrinsic quality or homogeneously distributed and the estimations are carried out using IRT(Item Response Theory). The system dynamically connects the test and the corresponding learning procedures. Test results are directly applied to estimate examinee's ability and are used to modify the item parameters and the difficulties of learning content objects during the learning procedure is being operated. We define the learning unit 'Node' as an amount of learning objects operated so that new parameters can be re-estimated. There are various content objects in a Node and the parameters estimated at the end of current Node are directly applied to the next Node. We offer the most appropriate learning Node for a person's ability throughout the estimation processes of IRT. As a result, this scheme improves learning efficiency in web-base e-Learning environments offering the most appropriate learning objects and items to the individual students according to their estimated abilities. This scheme can be applied to any e-Learning subject having homogeneous learning objects and unidimensional test items. In order to construct the system, we present an operation scenario using the proposed system architecture with the essential databases and agents.

• Communications for Statistical Applications and Methods
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• v.6 no.2
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• pp.611-620
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• 1999

We shall propose several estimators and confidence intervals for the scale parameter in a uniform distribution with the presence of a generalized uniform outlier and obtain mean squared errors(MSE) for their proposed estimators. And we shall compare numerical MSE's for the proposed several estimators of the scale parameter. Also we shall compare numerically expected lengths of confidence intervals of the scale parameter in a uniform distribution with the presence of a generalized uniform outlier.

• International Journal of Contents
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• v.5 no.1
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• pp.51-55
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• 2009

In this paper, we present a structure of personalized e-Learning system to study for a test formalized by uniform multiple-choice using on/off line mixed estimations as is the case of Driver :s License Test in Korea. Using the system a candidate can study toward the license through the Internet (and/or mobile instruments) within the personalized concept based on IRT(item response theory). The system accurately estimates user's ability parameter and dynamically offers optimal evaluation problems and learning contents according to the estimated ability so that the user can take possession of the license in shorter time. In order to establish the personalized e-Learning concepts, we build up 3 databases and 2 agents in this system. Content DB maintains learning contents for studying toward the license as the shape of objects separated by concept-unit. Item-bank DB manages items with their parameters such as difficulties, discriminations, and guessing factors, which are firmly related to the learning contents in Content DB through the concept of object parameters. User profile DB maintains users' status information, item responses, and ability parameters. With these DB formations, Interface agent processes user ID, password, status information, and various queries generated by learners. In addition, it hooks up user's item response with Selection & Feedback agent. On the other hand, Selection & Feedback agent offers problems and content objects according to the corresponding user's ability parameter, and re-estimates the ability parameter to activate dynamic personalized learning situation and so forth.