• Journal of the Korean Data and Information Science Society
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• v.24 no.4
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• pp.911-918
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• 2013

This study deals with the small sample likelihood based inference for the ratio of two normal variances. The small sample likelihood inference is an approximation method. The signed log-likelihood ratio statistic and the modified signed log-likelihood ratio statistic, which converge to standard normal distribution, are proposed for the normal variance ratio. Through the simulation study, the coverage probabilities of confidence interval and power of the exact, the signed log-likelihood and the modified signed log-likelihood ratio statistic will be compared. A real data example will be provided.

• East Asian mathematical journal
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• v.9 no.2
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• pp.235-239
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• 1993

• Journal of the Korean Statistical Society
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• v.18 no.1
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• pp.26-37
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• 1989

When we select the t best out of k populations in the indifference zone formulation, a lower confidence bound on the probability of a correct selection is derived for families with monotone likelihood ratio. The result is applied to the normal means problem when the variance is common, and to the normal variances problem. Tables to implement the confidence bound for the normal variances problem are provided.

• Proceedings of the Korean Statistical Society Conference
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• 2002.05a
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• pp.73-78
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• 2002

In this paper we develop a method for constructing a Bayesian HPD (highest probability density) interval of a ratio of two multivariate normal generalized variances. The method gives a way of comparing two multivariate populations in terms of their dispersion or spread, because the generalized variance is a scalar measure of the overall multivariate scatter. Fully parametric frequentist approaches for the interval is intractable and thus a Bayesian HPD(highest probability densith) interval is pursued using a variant of weighted Monte Carlo (WMC) sampling based approach introduced by Chen and Shao(1999). Necessary theory involved in the method and computation is provided.

• Journal of the Korean Statistical Society
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• v.24 no.1
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• pp.45-64
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• 1995

When a random sample is taken from a certain class of discrete and continuous distributions whose support depend on two parameters, we could find that there exists the complete and sufficient statistic for parameters which belong to a certain class, and fomulate the uniformly minimum variance unbiased estimator (UMVUE) of any estimable function. Some UMVUE's of parametric functions are illustrated for the class of the distribution. Especially, we find that the UMVUE of some estimable parametric function from the truncated normal distribution could be expressed by the version of the Mill's ratio.

• Journal of Biosystems Engineering
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• v.28 no.3
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• pp.261-268
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• 2003

Ten MHz pulsed NMR spectrometer was used to measure the magnetic resonance characteristics of Korean red ginseng. The difference in the internal structures of good and bad red ginsengs was examined by their NMR characteristics. Average values of $T_1$ and free induction decay(FID) ratios of under grade Korean red ginseng were the highest among the three groups categorized as normal, medium and under grades Korean red ginseng and average values of $T_2$ and $T_2$$^{＊}$ of them were the lowest among the three groups. Principal component analysis(PCA) was used to observe the contribution of measured NMR values to the grade of Korean red ginseng. The measured $T_1$, $T_2$, $T_2$$^{＊}$ and FID ratio of 79 Korean red ginsengs classified as normal grade, medium grade and under grade were examined using PCA analysis. Cumulative variance of PC1 through PC3 occupied more than 90% of total variance at first and second NMR measurement. Plots of PC scores for the most important PCs showed that normal red ginseng samples were distributed around the left region of PC1 axis and most of the undergrade red ginseng samples were scattered around the right region of PC1 axis.

• Communications for Statistical Applications and Methods
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• v.23 no.6
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• pp.563-574
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• 2016

In this study, we propose several simultaneous tests to detect the difference between means and variances for the two-sample problem when the underlying distribution is normal. For this, we apply the likelihood ratio principle and propose a likelihood ratio test. We then consider a union-intersection test after identifying the likelihood statistic, a product of two individual likelihood statistics, to test the individual sub-null hypotheses. By noting that the union-intersection test can be considered a simultaneous test with combination function, also we propose simultaneous tests with combination functions to combine individual tests for each sub-null hypothesis. We apply the permutation principle to obtain the null distributions. We then provide an example to illustrate our proposed procedure and compare the efficiency among the proposed tests through a simulation study. We discuss some interesting features related to the simultaneous test as concluding remarks. Finally we show the expression of the likelihood ratio statistic with a product of two individual likelihood ratio statistics.

• Computers and Concrete
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• v.27 no.5
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• pp.473-487
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• 2021

The review of the literature and design guidelines indicates a lack of design codes governing the shear strength of reinforced concrete (RC) beams strengthened with ultrahigh-performance fiber-reinforced concrete (UHPFRC). This study uses the results of a 3D finite element model constructed previously by the authors and verified against an experimental programme to gain a clear understanding of the shear strength of RC beams strengthened with UHPFRC by using different schemes. Experimental results found in the literature along with the numerical results for shear capacities of normal-strength RC and UHPFRC beams without stirrups are compared with available code design guidelines and empirical models found in the literature. The results show variance between the empirical models and the experimental results. Accordingly, proposed equations derived based on empirical models found in the literature were set to estimate the shear capacity of normal-strength RC beams without stirrups. In addition, the term 'shear span-to-depth ratio' is not considered in the equations for design guidelines found in the literature regarding the shear capacity of UHPFRC beams without stirrups. Consequently, a formula estimating the shear strength of UHPFRC and RC beams strengthened with UHPFRC plates and considering the effect of shear span-to-depth ratio is proposed and validated against an experimental programme previously conducted by the authors.

• Communications for Statistical Applications and Methods
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• v.10 no.3
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• pp.749-764
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• 2003

In this paper we explain that normal theory likelihood-ratio tests(z, t, $x^2$. F) for mean(s) or variance(s) can be geometrically related to volume of difference of two joint pdf's. One is an estimated joint pdf under null parameter space $\omega$ and the other is an estimated joint pdf under full parameter space $\Omega$. For explanations, ‘distance between two distributions’ is defined. We study properties of it, and derive some results on the distance between two multivariate normal distributions.

• Proceedings of the ESK Conference
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• 1996.04a
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• pp.301-306
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• 1996

Different patterns of dynamic trunk performance between normal subjects and low-back pain (LBP) patients have been investigated. Ten healthy subjects and ten LBP patients were recruited for this study. An experiment was designed to quantify the dynamic motion of the back and hip during repetitive flexion/extension of the trunk. The angular velocity, angular acceleration and the phase angle difference between the hip and back were recorded as dependent measures via electro- mechanical devices. Results showed the significant differences in the velocity and acceleration of the hip and back and the phase angle between normal subjects and LBP patients. The consistency of kinematic variables during motion cycles was also examined in terms of variance ratio (Hershler and Milner, 1978). Based on the results of the study, these quantifiable variables such as trunk kinematics and hip-spine coordination can be developed as a medical tool to identify LBP patients in addition to current imaging techniques.