• Communications for Statistical Applications and Methods
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• v.27 no.3
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• pp.349-363
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• 2020

Penalized spline is a suitable nonparametric approach in estimating mean model in small area. However, application of the approach in informative sampling in a published article is uncommon. We propose a semiparametric mixed-model using penalized spline under informative sampling to estimate mean of small area. The response variable is explained in terms of mean model, informative sample effect, area random effect and unit error. We approach the mean model by penalized spline and utilize a penalized spline function of the inclusion probability to account for the informative sample effect. We determine the best and unbiased estimators for coefficient model and derive the restricted maximum likelihood estimators for the variance components. A simulation study shows a decrease in the average absolute bias produced by the proposed model. A decrease in the root mean square error also occurred except in some quadratic cases. The use of linear and quadratic penalized spline to approach the function of the inclusion probability provides no significant difference distribution of root mean square error, except for few smaller samples.

• Speech Sciences
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• v.1
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• pp.237-259
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• 1997

Cleft Palate speech appears to have hyper/hyponasality with velopharyngeal insufficiency and articulation disorders. Previous studies on Cleft Palate speech have shown that speech tends to have lower airflow and air pressure. To examine the aerodynamic characteristics of Cleft Palate speech, Aerophone II Voice function Analyzer was used. We measured sound pressure level, airflow, air pressure and glottal power. Three Cleft Palate adults and five normal adults participated in this experiment. The test words are composed of: (1) the sustained vowel /o/ (2) /CiCi/, where C is one of three different stop consonants in Korean (3) /bimi/. Subjects were asked to produce /bimi/ five times without opening their lips. All the data was statistically tested by t-test for Cleft Palate patients before operation groups and control groups and paired t-test for Cleft Palate patients before and after operation groups. The results were as follow: (1) Cleft Palate patients generally speak with incomplete oral closure and lower oral air pressure. As a result, the SPL of Cleft Palate before operation is 3 dB lower than control groups. (2) Airflow of Cleft Palate in phonation and articulation is lower than that of control groups. However, it increased after operation. Lung volume and mean airflow in phonation are significantly increased (p<0.05). (3) Although velopharyngeal function (velar opening rate) of Cleft Palate is poor in comparison with control groups, it was recovered after operation. In this event maximum flow rate and mean airflow rate are significantly increased (p<0.05). (4) Air pressure of Cleft Palate in speech is lower than that of control groups. In general, the air pressure of Cleft Palate increased after operation. In this event air pressure of glottalized consonant is significantly increased (p<0.04). (5) Glottal Power(mean power, mean efficient and mean resistant) of Cleft Palate patients is lower than that of control groups. But mean efficient and mean resistant of Cleft Palate patients increased significantly (p<0.05) after operation.

• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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• pp.1085-1100
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• 2023

For any given function f, we focus on the so-called prescribed mean curvature problem for the measure e^-f(|x|2)dx provided thate^-f(|x|2) ∈ L¹(ℝⁿ⁺¹). More precisely, we prove that there exists a smooth hypersurface M whose metric is ds² = dρ² + ρ²d𝜉² and whose mean curvature function is ${\frac{1}{n}}(\frac{u^p}{{\rho}^{\beta}})e^{f({\rho}^2)}{\psi}(\xi)$ for any given real constants p, β and functions f and ψ where u and ρ are the support function and radial function of M, respectively. Equivalently, we get the existence of a smooth solution to the following quasilinear equation on the unit sphere 𝕊ⁿ, $${\sum_{i,j}}({{\delta}_{ij}-{\frac{{\rho}_i{\rho}_j}{{\rho}^2+|{\nabla}{\rho}|^2}})(-{\rho}ji+{\frac{2}{{\rho}}}{\rho}j{\rho}i+{\rho}{\delta}_{ji})={\psi}{\frac{{\rho}^{2p+2-n-{\beta}}e^{f({\rho}^2)}}{({\rho}^2+|{\nabla}{\rho}|^2)^{\frac{p}{2}}}}$$ under some conditions. Our proof is based on the powerful method of continuity. In particular, if we take $f(t)={\frac{t}{2}}$, this may be prescribed mean curvature problem in Gauss measure space and it can be seen as an embedded result in Gauss measure space which will be needed in our forthcoming papers on the differential geometric analysis in Gauss measure space, such as Gauss-Bonnet-Chern theorem and its application on positive mass theorem and the Steiner-Weyl type formula, the Plateau problem and so on.

• Journal of the Korean Data and Information Science Society
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• v.22 no.1
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• pp.89-97
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• 2011

The aims of this study were to propose a method of estimation for mean residual life function (MRLF) from conditional survival function using the Buckley and James's (1979) pseudo random variables, and then to assess the performance of the proposed method through the simulation studies. The mean squared error (MSE) of proposed method were less than those of the Cox's proportional hazard model (PHM) and Beran's nonparametric method for non-PHM case. Futhermore in the case of PHM, the MSE's of proposed method were similar to those of Cox's PHM. Finally, to evaluate the appropriateness of practical use, we applied the proposed method to the gastric cancer data. The data set consist of the 1, 192 patients with gastric cancer underwent surgery at the Department of Surgery, K-University Hospital.

• Annals of Rehabilitation Medicine
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• v.41 no.6
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• pp.924-934
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• 2017

Objective To investigate the anatomical correlates of the neuropsychological deficits in patients with the cerebellar stroke. Methods We screened patients who were admitted to the National Rehabilitation Center with the cerebellar stroke between October 2012 and November 2016. The patients with the cerebellar stroke who underwent neuropsychological testing for which the Seoul Neuropsychological Screening Battery (SNSB) or the SNSB-II were enrolled. The neuropsychological function capacities were compared in accordance with the stroke type (hemorrhagic vs. ischemic) and the location (right/left anterior, right/left posterior intermediate, right/left posterior lateral lobe, and vermis). Mean z-scores were computed to compare the patient performances with the population averages. Results Twenty-six patients (15 with ischemic stroke and 11 with hemorrhagic stroke) with a mean age of $54.8{\pm}16.6$ years were assessed $8.8{\pm}9.2$ months after the stroke. Differences in the neuropsychological functioning according to the stroke type were not observed. All of the numerical subtests of the stroke patients showed significantly poorer performances compared with the population averages (mean z-score <0), and some of the subtests revealed abnormal performances in attention-, visuospatial function-, memory-, and frontal/executive function-related tasks (mean z-score <-1). The patients with the presence of a lesion in the right posterior intermediate lobe of the cerebellum showed a poorer performance in the subtests evaluating the executive function including the Korean-version Stroop Test (p=0.04), the Digit Symbol Coding Test (p=0.01), and the Korean-version Trail Making Test (p=0.02) compared with the patients without that lesion. Conclusion The present study confirms that the cerebellar stroke affects the neuropsychological functioning which is associated with the anatomical site of stroke.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.44 no.1
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• pp.45-50
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• 2021

Machines and facilities are physically or chemically degenerated by continuous usage. The representative type of the degeneration is the wearing of tools, which results in the process mean shift. According to the increasing wear level, non-conforming products cost and quality loss cost are increasing simultaneously. Therefore, a preventive maintenance is necessary at some point. The problem of determining the maintenance period (or wear limit) which minimizes the total cost is called the 'process mean shift problem'. The total cost includes three items: maintenance cost (or adjustment cost), non-conforming cost due to the non-conforming products, and quality loss cost due to the difference between the process target value and the product characteristic value among the conforming products. In this study, we set the production volume as a decreasing function rather than a constant. Also we treat the process variance as a function to the increasing wear rather than a constant. To the quality loss function, we adopted the Cpm+, which is the left and right asymmetric process capability index based on the process target value. These can more reflect the production site. In this study, we presented a more extensive maintenance model compared to previous studies, by integrating the items mentioned above. The objective equation of this model is the total cost per unit wear. The determining variables are the wear limit and the initial process setting position that minimize the objective equation.

• Journal of the Korean Statistical Society
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• v.26 no.2
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• pp.199-210
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• 1997

Using regression methods based on quasi-likelihood equation, one only needs to specify the conditional mean and variance functions for the response variable in the analysis. In this paper, an omnibus lack-of-fit test is proposed to test the validity of these two functions. Our test is consistent against the alternative under which either the mean or the variance is not the one specified in the null hypothesis. The large-sample null distribution of our test statistics can be approximated through simulations. Extensive numerical studies are performed to demonstrate that the new test preserves the prescribed type I error probability. Power comparisons are conducted to show the advantage of the new proposal.

• Journal of Korea Society of Digital Industry and Information Management
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• v.16 no.3
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• pp.49-58
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• 2020

Image interpolation, a technology that converts low resolution images into high resolution images, has been widely used in various image processing fields such as CCTV, web-cam, and medical imaging. This technique is based on the fact that the statistical distributions of the white Gaussian noise and the difference between the interpolated image and the original image is similar to each other. The proposed algorithm is composed of three steps. In first, the interpolated image is derived by random image interpolation. In second, we derive weighting functions that are used to apply non-local mean filtering. In the final step, the prediction error is corrected by performing non-local mean filtering by applying the selected weighting function. It can be considered as a post-processing algorithm to further reduce the prediction error after applying an arbitrary image interpolation algorithm. Simulation results show that the proposed method yields reasonable performance.

• International Journal of Reliability and Applications
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• v.7 no.2
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• pp.155-166
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• 2006

Many software reliability growth models (SRGMs) based on nonhomogeneous Poisson process (NHPP) have been developed and applied in practice. NHPP SRGMs are characterized by their mean value functions. Mean value functions are usually derived from differential equations representing the fault detection/removal process during testing. In this paper such differential equations are regarded as frameworks for generating mean value functions. Currently available frameworks are theoretically discussed with respect to capability of representing the fault detection/removal process. Then two general frameworks are proposed.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.487-494
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• 2016

Let p be an odd prime and c be a fixed integer with (c, p) = 1. For each integer a with $1{\leq}a{\leq}p-1$, it is clear that there exists one and only one b with $0{\leq}b{\leq}p-1$ such that $ab{\equiv}c$ mod p. Let N(c, p) denote the number of all solutions of the congruence equation $ab{\equiv}c$ mod p for $1{\leq}a$, $b{{\leq}}p-1$ in which a and $\bar{b}$ are of opposite parity, where $\bar{b}$ is defined by the congruence equation $b{\bar{b}}{\equiv}1$ mod p. The main purpose of this paper is using the mean value theorem of Dirichlet L-functions and the properties of Gauss sums to study the computational problem of one kind mean value function related to $E(c,p)=N(c,p)-{\frac{1}{2}}{\phi}(p)$, and give its an exact computational formula.