• Journal of Computing Science and Engineering
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• v.7 no.2
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• pp.99-111
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• 2013

Approximating a divergence between two probability distributions from their samples is a fundamental challenge in statistics, information theory, and machine learning. A divergence approximator can be used for various purposes, such as two-sample homogeneity testing, change-point detection, and class-balance estimation. Furthermore, an approximator of a divergence between the joint distribution and the product of marginals can be used for independence testing, which has a wide range of applications, including feature selection and extraction, clustering, object matching, independent component analysis, and causal direction estimation. In this paper, we review recent advances in divergence approximation. Our emphasis is that directly approximating the divergence without estimating probability distributions is more sensible than a naive two-step approach of first estimating probability distributions and then approximating the divergence. Furthermore, despite the overwhelming popularity of the Kullback-Leibler divergence as a divergence measure, we argue that alternatives such as the Pearson divergence, the relative Pearson divergence, and the $L^2$-distance are more useful in practice because of their computationally efficient approximability, high numerical stability, and superior robustness against outliers.

• Bulletin of the Korean Chemical Society
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• v.23 no.2
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• pp.189-194
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• 2002

Two-photon resonant third photon ionization of atomic bromine $(4p^5\;^2P_{3/2}\;and\;^2P_{1/2})$ has been studied using a photoelectron imaging spectroscopy in the wavelength region 250 - 278 nm. The technique has yielded simultaneously both relative branching ratios to the three levels of $Br^+(^3P_2,\;^3P_{0.1}\;and^1D_2)$ with $4p^4$ configuration and the angular distributions of outgoing photoelectrons. The product branching ratios reveal a strong propensity to populate particular levels in many cases. Several pathways have been documented for selective formation of $Br^+(^3P_2)$ and $Br^+(^3P_{0.1})$ ions. In general, the final ion level distributions are dominated by the preservation of the ion core configuration of a resonant excited state. Some deviations from this simple picture are discussed in terms of the configuration interaction of resonant states and the autoionization in the continuum. The photoelectron angular distributions are qualitatively similar for all transitions, with a positive $A_2$ anisotropy coefficient of 1.0-2.0 and negligible $A_4$ in most cases, which suggests that the angular distribution is mainly determined by the single-photon ionization process of a resonant excited state induced from the third photon absorption.

• IE interfaces
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• v.17 no.1
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• pp.1-12
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• 2004

In a modern semiconductor device manufacturing industry, statistical bin limits on wafer level test bin data are used for minimizing value added to defective product as well as protecting end customers from potential quality and reliability excursion. Most wafer level test bin data show skewed distributions. By Monte Carlo simulation, this paper evaluates methods and sample size effect regarding determination of statistical bin limits. In the simulation, it is assumed that wafer level test bin data follow the Poisson distribution. Hence, typical shapes of the data distribution can be specified in terms of the distribution's parameter. This study examines three different methods; 1) percentile based methodology; 2) data transformation; and 3) Poisson model fitting. The mean square error is adopted as a performance measure for each simulation scenario. Then, a case study is presented. Results show that the percentile and transformation based methods give more stable statistical bin limits associated with the real dataset. However, with highly skewed distributions, the transformation based method should be used with caution in determining statistical bin limits. When the data are well fitted to a certain probability distribution, the model fitting approach can be used in the determination. As for the sample size effect, the mean square error seems to reduce exponentially according to the sample size.

• Honam Mathematical Journal
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• v.42 no.4
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• pp.795-809
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• 2020

In the present paper, we introduce the notion of quasi hemi-slant submanifolds of almost Hermitian manifolds and give some of its examples. We obtain the necessary and sufficient conditions for the distributions to be integrable. We also investigate the necessary and sufficient conditions for these submanifolds to be totally geodesic and study the geometry of foliations determined by the distributions. Finally, we obtain the necessary and sufficient condition for a quasi hemi-slant submanifold to be local product of Riemannian manifold.

• Journal of the Korean Operations Research and Management Science Society
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• v.14 no.2
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• pp.67-74
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• 1989

This paper considers single-product production and inventory management problem where cumulative demands up to each time period are mutually independent random variables(known) having continuous probability distributions and the associated cost-minimizing production schedule (when to produce and how much to produce) need be determined in rolling horizon environment. For the problem, both the production cost and the inventory holding and backlogging costs are included in the whole system cost. The probability distributions of these costs are expressed in terms of random demands, and utilized to exploit a solution procedure for a production schedule which minimizes the expected unit time system cost and also reduces the probability of rist that, for the first-period of each production cycle (rolling horizon), the cost of the "production" option will exceed that of the "non-production" one. Numerical examples are presented for the solution procedure illustration.cedure illustration.

• International Journal of Reliability and Applications
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• v.4 no.4
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• pp.171-181
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• 2003

This paper proposes a U-test statistic for the problem of testing that a life distribution is exponential against the alternative that it is harmonic new better (worse) than used in expectation upper tail HNBUET (HNWUET), but not exponential on complete data. Selected critical values are tabulated for sample sizes n =5(1)60. The asymptotic normality of the statistic is proved and a comparison is made of the asymptotic efficiency between the statistic and other statistics. The power of the test is studied by simulation. A test for HNBUET in the case of randomly right-censored data is also considered. An application of the proposed test statistic in medical sciences is given.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2005.11a
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• pp.205-208
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• 2005

We have fuzzy hypotheses testing from Bayesian statistics with ideas from fuzzy sets theory to generalize Bayesian methods both for samples of fuzzy data and for prior distributions with non-precise parameters. Appling the principle of agreement index, the posterior odds ratio in the favor of hypotheses $H_0$ is equal to product of the fuzzy odds ratio and the fuzzy likelihood ratio. If the Posterior odds ratio exceeds the grade judgement, we accept the hypothesis $H_0$ for the degree.

• Proceedings of the KSME Conference
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• 2003.11a
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• pp.1834-1839
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• 2003

Temperature and velocity distributions of hot air flows in rotational molding machines with two different shapes and structures of oven and inlet were investigated by using FLUENT, a commercial computational fluid dynamics code. The shape and structure of oven and inlet in current rotational molding machine were improved. Two different sizes of mold inside each oven were considered in the analysis. Temperature and velocity distributions of hot air flows in two different rotational molding machines were compared to each other. In order to reduce cycle time and improve product quality in current rotational molding machine, the improved shape and structure of oven and inlet were proposed.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.9
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• pp.2234-2244
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• 1994

A process sequence of multi-operation cold forging for actual application in industry is designed with the rigid-plastic finite element method to form a constant velocity joint housing(CVJ housing). The material flow during the CVJ housing forming is axisymmetric until the final forging process for forming of ball grooves. This study treats the deformation as an axisymmetric case. The main objective of the process sequence design is to obtain preforms which satisfy the design criteria of near-net-shape product requiring less machining after forming. The process sequence design also investigates velocity distributions, effective strain distributions and forging loads, which are useful information in the real process design.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1995.10a
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• pp.48-56
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• 1995

A manufacturing process for the axle-housing is analyzed by the rigid-plastic finite element method. The process contains five stages for the final product. During the simulation, remeshings are done four times due to severe mesh distributions. FE Analysis is performed mainly for strain distributions and load-stroke relationships. Those results are to be an useful design criteria for designing a new process sequence in future.