• Journal of the Korean Data and Information Science Society
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• v.24 no.3
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• pp.643-650
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• 2013

We develop noninformative priors for a ratio of parameters of two Maxwell distributions which is used to check the equality of two Maxwell distributions. Specially, we focus on developing probability matching priors and Je reys' prior for objectiv Bayesian inferences. The probability matching priors, under which the probability of the Bayesian credible interval matches the frequentist probability asymptotically, are developed. The posterior propriety under the developed priors will be shown. Some simulations are performed for identifying the usefulness of proposed priors in objective Bayesian inference.

• Communications for Statistical Applications and Methods
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• v.25 no.6
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• pp.633-645
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• 2018

Gaussian error distributions are a common choice in traditional regression models for the maximum likelihood (ML) method. However, this distributional assumption is often suspicious especially when the error distribution is skewed or has heavy tails. In both cases, the ML method under normality could break down or lose efficiency. In this paper, we consider the log-concave and Gaussian scale mixture distributions for error distributions. For the log-concave errors, we propose to use a smoothed maximum likelihood estimator for stable and faster computation. Based on this, we perform comparative simulation studies to see the performance of coefficient estimates under normal, Gaussian scale mixture, and log-concave errors. In addition, we also consider real data analysis using Stack loss plant data and Korean labor and income panel data.

• Proceedings of the Korea Air Pollution Research Association Conference
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• 2006.04a
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• pp.55-56
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• 2006

This thesis describes the use of measured aerosol size distributions and size-resolved hygroscopic growth to examine the physical and chemical properties of several particle classes. The primary objective of this work was to investigate the optical and cloud forming properties of a range of ambient aerosol types measured in a number of different locations. The tool used for most of these analyses is a differential mobility analyzer / tandem differential mobility analyzer (DMA / TDMA) system developed in our research group. To collect the data described in two of the chapters of this thesis, an aircraft-based version of the DMA / TDMA was deployed to Japan and California. The data described in two other chapters were conveniently collected during a period when the aerosol of interest came to us. The unique aspect of this analysis is the use of these data to isolate the size distributions of distinct aerosol types in order to quantify their optical and cloud forming properties. I used collected data during the Asian Aerosol Characterization Experiment (ACE-Asia) to examine the composition and homogeneity of a complex aerosol generated in the deserts and urban regions of China and other Asian countries. An aircraft-based tandem differential mobility analyzer was used for the first time during this campaign to examine the size-resolved hygroscopic properties of particles having diameters between 40 and 586 nm. Asian Dust Above Monterey (ADAM-2003) study was designed both to evaluate the degree to which models can predict the long-range transport of Asian dust, and to examine the physical and optical properties of that aged dust upon reaching the California coast. Aerosol size distributions and hygroscopic growth are measured in College Station, TX to investigate the cloud nucleating and optical properties of a biomass burning aerosol generated from fires on the Yucatan Peninsula. Measured aerosol size distributions and size-resolved hygroscopicity and volatility were used to infer critical supersaturation distributions of the distinct particle types that were observed during this period. The predicted CCN concentrations were used in a cloud model to determine the impact of the different aerosol types on the expected cloud droplet concentration. RH-dependent aerosol extinction coefficients are calculated at a wavelength of 550 nm.

• Journal of Applied Reliability
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• v.17 no.3
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• pp.213-223
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• 2017

Purpose: The purpose of this study is to arrange the life data analysis literatures based on the Bayesian method quantitatively and provide it as tables. Methods: The Bayesian method produces a more accurate estimates of other traditional methods in a small sample size, and it requires specific algorithm and prior information. Based on these three characteristics of the Bayesian method, the criteria for classifying the literature were taken into account. Results: In many studies, there are comparisons of estimation methods for the Bayesian method and maximum likelihood estimation (MLE), and sample size was greater than 10 and not more than 25. In probability distributions, a variety of distributions were found in addition to the distributions of Weibull commonly used in life data analysis, and MCMC and Lindley's Approximation were used evenly. Finally, Gamma, Uniform, Jeffrey and extension of Jeffrey distributions were evenly used as prior information. Conclusion: To verify the characteristics of the Bayesian method which are more superior to other methods in a smaller sample size, studies in less than 10 samples should be carried out. Also, comparative study is required by various distributions, thereby providing guidelines necessary.

• Communications for Statistical Applications and Methods
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• v.28 no.6
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• pp.595-610
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• 2021

Recently a few articles have derived robust first-order rotatable and D-optimal designs for the lifetime response having distributions gamma, lognormal, Weibull, exponential assuming errors that are correlated with different correlation structures such as autocorrelated, intra-class, inter-class, tri-diagonal, compound symmetry. Practically, a first-order model is an adequate approximation to the true surface in a small region of the explanatory variables. A second-order model is always appropriate for an unknown region, or if there is any curvature in the system. The current article aims to extend the ideas of these articles for second-order models. Invariant (free of the above four distributions) robust (free of correlation parameter values) second-order rotatable designs have been derived for the intra-class and inter-class correlated error structures. Second-order rotatability conditions have been derived herein assuming the response follows non-normal distribution (any one of the above four distributions) and errors have a general correlated error structure. These conditions are further simplified under intra-class and inter-class correlated error structures, and second-order rotatable designs are developed under these two structures for the response having anyone of the above four distributions. It is derived herein that robust second-order rotatable designs depend on the respective error variance covariance structure but they are independent of the correlation parameter values, as well as the considered four response lifetime distributions.

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.467-482
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• 2000

Testing equality of two and k distributions has long been an interesting issue in statistical inference. To overcome the sparseness of data points in high-dimensional space and deal with the general cases, we suggest several projection pursuit type statistics. Some results on the limiting distributions of the statistics are obtained, some properties of Bootstrap approximation are investigated. Furthermore, for computational reasons an approximation for the statistics the based on Number theoretic method is applied. Several simulation experiments are performed.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.111-118
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• 2013

External excitations are employed to investigate properties of optical media, with measurement data often analyzed via linear response theory. In this respect, external forcing is modeled here by well-known Poisson and negative-binomial distributions. Ensuing dynamics is examined with a special attention to the relative decay rates of damped harmonic oscillators to such external forcing, along with its relationship to other physical phenomena.

• 한국데이터정보과학회:학술대회논문집
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• 2005.10a
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• pp.27-34
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• 2005

We consider the problem of estimating the system reliability noninformative priors when both stress and strength follow generalized gamma distributions. We first derive Jeffreys' prior, group ordering reference priors, and matching priors. We investigate the propriety of posterior distributions and provide marginal posterior distributions under those noninformative priors. We also examine whether the reference priors satisfy the probability matching criterion.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 1996.03a
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• pp.47-51
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• 1996

Unsteady-state temperature distributions and thermal deformations of a spindle system are studied in this paper. Three dimensional model is built for analysis, and the amount of heat generation of bearing and the thermal characteristic values including heat transfer coefficient are estimated. Temperature distributions and thermal deformations of a model are analyzed using the finite element method and the termal boundary values. Numerical results are compared with the measured data. The results show that thermal deformations and temperature distributions of a high precision spindle system can be reasonably estimated using the three dimensional model and the finite element method.

• Bulletin of the Korean Chemical Society
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• v.21 no.5
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• pp.493-496
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• 2000

By use of the rotational distribution expression previously derived based on the collisional time correlation function formalism, the rotational distributions of $CO_2$ vibrational ground state (00°0) after collisions with hot H, D, or Cl atom have been constructed. Energy and rotational quantum number parameters which can characterize the rotational distributions are also calculated and compared with those deduced from the experimental distribution. The results from this work would be very useful in predicting the rotational distributions in the lower J region for which experimental data are not available due to the interference from the ambient $CO_2$.