• Communications for Statistical Applications and Methods
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• v.21 no.6
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• pp.539-559
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• 2014

We derive the exact distribution of summation for random samples from uniform distribution and then compare the exact distribution with the approximated normal distribution obtained by the central limit theorem. To check the similarity between two distributions, we consider five existing normality tests based on the difference between the target normal distribution and empirical distribution: Anderson-Darling test, Kolmogorov-Smirnov test, Cramer-von Mises test, Shapiro-Wilk test and Shaprio-Francia test. For the purpose of comparison, those normality tests are applied to the simulated data. It can sometimes be difficult to derive an exact distribution. Thus, we try two different transformations to find out which transform is easier to get the exact distribution in terms of calculation complexity. We compare two transformations and comment on the advantages and disadvantages for each transformation.

• Korean Management Science Review
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• v.24 no.1
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• pp.77-90
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• 2007

Taguchi assumed that a product characteristic has the uniform distribution in its preventive maintenance limit when deriving the expected loss generated by the quality deviation. But it is reasonable to assume that a product characteristic has the normal distribution than the uniform distribution. On this paper, we first find the optimum inspection interval and the optimum preventive maintenance limit under the truncated triangular distribution. Secondly we use the beta-general distribution and compare with the truncated triangular distribution. By using the numerical examples, we find the optimum inspection interval and the optimum preventive maintenance limit under their distributions. As a result, we find that the beta-general distribution gives the best solution and easy calculation.

• Journal of Korean Society for Quality Management
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• v.26 no.3
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• pp.60-70
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• 1998

When driving the expected loss generated by the quality deviation, Taguchi(1991b) assumed that an objective characteristic has the uniform distribution in its control limit. But it is reasonable to assume that an objective characteristic has the normal distribution than the uniform distribution. Since the triangular distribution is similar to the normal distribution and easy to handle as well, in this article, we first find the optimum measurement interval and the optimum control limit under the triangular distribution. Under the normal assumption, the modified method is compared to Taguchi's. Secondly we find the numerical value solution of the optimum measurement interval and the optimum control limit under the normal distribution.

• Proceedings of the Korean Geotechical Society Conference
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• 2000.03b
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• pp.663-668
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• 2000

In this study, the Atterberg limit and grain-size analysis were carried for the purpose of investigating the influence on drying and organic matter of Ulsan marine deposited clay. The results revealed that Atterberg limit was decreased and grain-size distribution was variable on drying. The presence of organic matter also influenced on the physical properties of the soils. The physical properties of marine deposited clay were variable on drying, so that we recommended grain-size analysis and Atterberg limit test were performed under the wet condition of the soils after sampling.

• Korean Journal of Plant Taxonomy
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• v.40 no.4
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• pp.267-273
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• 2010

The distribution of three typical warm-temperate evergreen trees, Quercus acuta Thunb., Neolitsea sericea (Blume) Koidz., and Machilus thunbergii Siebold & Zucc., were surveyed on the Korean Peninsula based on field and specimen investigations and the distribution maps of the three species were prepared. The distribution patterns of the species correspond to the south coast floristic region in Korea, which includes the distributional areas of Jeju-do, Isl. Ulleung, the southern coastal areas, and the areas up to the islands around Incheon in the Yellow Sea. The northernmost limit of the distribution of Quercus acuta is Isl. Nap of Incheon in the west, and a new distribution was found at Isl. Ulleung in the East Sea; additionally, the limit of Neolitsea sericea is the Deojoek archipelago of Incheon. The northernmost limit of Machilus thunbergii is Isl. Daecheong of Incheon, which is the highest latitude among those of the three species. This distribution survey of evergreen broad-leaved trees in Korea can be used as basic data for the delimitation of floristic regions and as a bio-indicator of climatic change.

• Proceedings of the Korea Water Resources Association Conference
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• 2016.05a
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• pp.201-201
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• 2016

The asymptotic extreme value distributions of maxima are a natural choice when designing against future extreme events like flood peaks or wave heights, given a stationary time series. The generalized extreme value distribution (GEV) is often utilised in this context because it is seen as a convenient single expression for extreme event analysis. However, the GEV has a drawback because the location of the distribution bound relative to the data is a discontinuous function of the GEV shape parameter. That is, for annual maxima approximated by the Gumbel distribution, the data is also consistent with a GEV distribution with an upper bound (no lower bound) or a GEV distribution with a lower bound (no upper bound). A more consistent single extreme value expression for design purposes is proposed as the Weibull distribution of smallest extremes, as applied to transformed annual maxima. The Weibull distribution limit holds here for sufficiently large sample sizes, irrespective of the extreme value domain of attraction applicable to the untransformed maxima. The Gumbel, Type 2, and Type 3 extreme value distributions thus become redundant, together with the GEV, because in reality there is only a single asymptotic extreme value distribution required for design purposes - the Weibull distribution of minima as applied to transformed maxima. An illustrative synthetic example is given showing transformed maxima from the normal distribution approaching the Weibull limit much faster than the untransformed sample maxima approach the normal distribution Gumbel limit. Some New Zealand examples are given with the Weibull distribution being applied to reciprocal transformations of annual flood maxima, where the untransformed maxima follow apparently different extreme value distributions.

• Journal of the Korean Mathematical Society
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• v.36 no.5
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• pp.923-943
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• 1999

In this paper we consider functionals of the empirical age distribution of supercritical Bellman-Harris processes. Let f : R+ longrightarrow R be a measurable function that integrates to zero with respect to the stable age distribution in a supercritical Bellman-Harris process with no extinction. We present sufficient conditions for the asymptotic normality of the mean of f with respect to the empirical age distribution at time t.

• Journal of Korean Society for Quality Management
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• v.25 no.1
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• pp.182-192
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• 1997

The well-known standard normal distribution has been used within the limit of standard variable value of u=3.59. However, the probability values above the limit are not given in the literature. In this study, a probability computation program for standard normal distribution to u=5.99 with the proportional normal distribution a, pp.oximation suggested by Abramowitz and Stegun, Hastings is developed. The new standard normal distribution table developed by the program is presented and will be of help to estimate of probability values for testing and estimation of process mean value, lot acceptable probability, defective percentage of PPM unit of an out-of specification limit, process capability, test power of control charts, probability and statistics.

• Journal of the Korean Statistical Society
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• v.25 no.4
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• pp.545-556
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• 1996

In this paper, we introduce a new concept of partial ordering which permits us to compare pairs of the dependence structures of a new hitting times for POD multivariate vector process of interest as to their degree of POD-ness. We show that POD ordering is closed under convolution, limit in distribution, compound distribution, mixture of a certain type and convex combination. Finally, we present several examples of POD ordering processes.

• Communications of the Korean Mathematical Society
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• v.14 no.3
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• pp.627-633
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• 1999

Let the given distribution $\pi$ have a log-concave density which is proportional to exp(-V(x)) on $R^d$. We consider a Markov chain induced by the method Gibbs sampling having $\pi$ as its in-variant distribution and prove geometric ergodicity and the functional central limit theorem for the process.