• Communications for Statistical Applications and Methods
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• v.10 no.3
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• pp.647-654
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• 2003

Bayesian probability models for finite populations are considered assuming so-called the super-population. We find the posterior distribution of population mean by a new approach, using the concept of pivotal quantity for the small sample case. A large sample theory is also treated throught the concept of asymptotically pivotal quantity.

• Proceedings of the Korean Statistical Society Conference
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• 2005.05a
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• pp.13-15
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• 2005

In this paper, we propose an extension of the maximum likelihood seasonal cointegration procedure developed by Johansen and Schaumburg (1999) for daily time series. We presented the finite sample distribution of the associated rank test statistics for daily data.

• Journal of the korean academy of Pediatric Dentistry
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• v.25 no.4
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• pp.717-730
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• 1998

The Finite Element Analysis has been used for stress analysis of prosthesis, orthodontic or orthopedic appliances and filling materials. The primary purpose of the present studying was to evaluate the effectiveness of needle post in promoting the retention and integrity of composite crown restored on the pulpotomized primary central incisor. Three finite element models-natural tooth (Sample I), composite crown with (Sample II) and without (Sample III) needle post-were constructed and the stress distribution within each model were analyzed and compared one another. The results can be summarized as follows: 1. In sample I, the stress was shown to have distributed uniformly throughout the whole tooth even to the alveolar bone. 2. In sample II, the transmission of stress from the crown to the root area was shown to be very poor and irregular. 3. In sample III, the needle post was proved to be very effective in distributing the stress well to the aveolar bone which might help in maintaining the stability of crown restoration.

• Journal of the Korean Statistical Society
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• v.28 no.1
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• pp.57-72
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• 1999

Falk(1994) showed that the asymptotic efficiency of the Pickands estimator of the extreme value index $\beta$ can considerably be improved by a simple convex combination. In this paper we propose an alternative estimator of $\beta$ which is as asymptotically efficient as the optimal convex combination of the Pickands estimators but has a better finite-sample performance. We prove consistency and asymptotic normality of the proposed estimator. Monte Carlo simulations are conducted to compare the finite-sample performances of the proposed estimator and the optimal convex combination estimator.

• Journal of Korean Institute of Industrial Engineers
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• v.41 no.1
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• pp.115-120
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• 2015

Evaluating product quality level is necessary before the manufactured items are delivered to the customer. When the amount of the items to be manufactured is limited and the product is of high price and should be evaluated by destructive testing, the number of samples to be tested should be as small as possible. This paper presents a small-sample inspection method using hyper-geometric distribution and Bayesian approach for finite small-sized population. A method of determining the minimum sample size is presented for given population size, allowable number of defectives, warranteed defective level, and confidence level which is the degree of confidence on the product quality level recognized by both the producer and the customer.

• Journal of the Korean Data and Information Science Society
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• v.9 no.2
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• pp.289-298
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• 1998

We investigate the distribution of likelihood ratio test(LRT) of null hypothesis a sample is from single gamma with unknown shape and scale against the alternative hypothesis a sample is from a mixture of two gammas, each with unknown scale and unknown (but equal) scale. To obtain stable maximum likelihood estimates(MLE) of a mixture of two gamma distributions, the EM(Dempster, Laird, and Robin(1977))and Modified Newton(Jensen and Johansen(1991)) algorithms were implemented. Based on EM, we made a simple structure likelihood equation for each parameter and could obtain stable solution by Modified Newton Algorithms. Simulation study was conducted to investigate the distribution of LRT for sample size n = 25, 50, 75, 100, 50, 200, 300, 400, 500 with 2500 replications. To determine the small sample distribution of LRT, I considered the model of a gamma distribution with shape parameter equal to 1 + f(n) and scale parameter equal to 2. The simulation results indicate that the null distribution is essentially invariant to the value of the shape parameter. Modeling of the null distribution indicates that it is well approximated by a gamma distribution with shape parameter equal to the quantity $0.927+1.18/\sqrt{n}$ and scale parameter equal to 2.16.

• Journal of the Korean Statistical Society
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• v.24 no.2
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• pp.303-312
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• 1995

We consider the following type of general semi-parametric non-linear regression model : $y_i = f_i(\theta) + \epsilon_i, i=1, \cdots, n$ where ${f_i(\cdot)}$ represents the set of non-linear functions of the unknown parameter vector $\theta' = (\theta_1, \cdots, \theta_p)$ and ${\epsilon_i}$ represents the set of measurement errors with unknown distribution. Under suitable finite-sample, small-dispersion asymptotic framework, we derive a general lower bound for the asymptotic mean squared error (AMSE) matrix of the Gauss-consistent estimator of $\theta$. We then prove the fundamental result that the general non-linear least squares estimator (NLSE) is an optimal estimator within the class of all regular Gauss-consistent estimators irrespective of the type of the distribution of the measurement errors.

• Communications for Statistical Applications and Methods
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• v.7 no.2
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• pp.385-392
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• 2000

Many tests for multivariate normality are based on the spherical coordinates of the scaled residuals of multivariate observations. Moore and Stubblebine's (1981) Pearson chi-square test is based on the radii of the scaled residuals, or equivalently the sample Mahalanobis distances of the observations from the sample mean vector. The chi-square statistic does not have a limiting chi-square distribution since the unknown parameters are estimated from ungrouped data. We will derive a simple closed form of the Rao-Robson chi-square test statistic and provide a self-contained proof that it has a limiting chi-square distribution. We then provide an illustrative example of application to a real data with a simulation study to show the accuracy in finite sample of the limiting distribution.

• Nuclear Engineering and Technology
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• v.33 no.1
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• pp.62-72
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• 2001

The one-dimensional finite element program was developed to analyze the coupled behavior of heat, moisture, and air transfer in unsaturated porous media. By using this program, the simulation results were compared with those from the laboratory infiltration tests under isothermal condition and temperature gradient condition, respectively. The discrepancy of water uptake was found in the upper region of a bentonite sample under isothermal condition between numerical simulation and laboratory experiment. This indicated that air pressure was built up in the bentonite sample which could retard the infiltration velocity of liquid. In order to consider the swelling phenomena of compacted bentonite which cause the discrepancy of the distribution of water content and temperature, swelling and shrinkage factors were incorporated into the finite element formulation. It was found that these factors could be effective to represent the moisture diffusivity and unsaturated hydraulic conductivity due to volume change of bentonite sample.

• Journal of Magnetics
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• v.15 no.4
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• pp.190-193
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• 2010

The design of joints in a transformer core significantly affects the transformer's efficiency. Air gaps cause variations in the flux distribution at the joints of the laminations, which depend on the geometry. Two similar samples consisting of electrical steel strips and amorphous ribbons were made. The spatial flux distributions were determined using an array of search coils for each sample. 2D models of these samples were created and examined by finite element analysis. The magnetic flux distribution for each lamination in the samples was computed. The results show that the flux density in amorphous ribbons above and below the air gap starts to approach saturation at lower flux density levels than for electrical steel. The flux density measured using the search coil under the air gap is increased in amorphous ribbons and decreased in the electrical steel with increasing frequency.