• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.605-618
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• 2018

The main goal of this paper is to study an extension of random summations of independent and identically distributed random variables when the number of summands in random summation is a partial sum of n independent, identically distributed, non-negative integer-valued random variables. Some characterizations of random summations are considered. The central limit theorems and weak law of large numbers for extended random summations are established. Some weak limit theorems related to geometric random sums, binomial random sums and negative-binomial random sums are also investigated as asymptotic behaviors of extended random summations.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.26 no.3
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• pp.183-189
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• 2013

In this paper, uncertainties and failure criteria of structure are mathematically expressed by random variables and a limit state equation. A limit state equation is approximated by Fleishman's 3rd order polynomials and the theoretical moments of an approximated limit state equation are calculated. Fleishman introduced a 3rd order polynomial in terms of only standard normal distiribution random variables. But, in this paper, Fleishman's polynomial is extended to various random variables including beta, gamma, uniform distributions. Cumulants and a normalized limit state equation are used to calculate a theoretical moments of a limit state equation. A cumulative distribution function of a normalized limit state equation is approximated by a Pearson system.

• Journal of the Korean Statistical Society
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• v.11 no.2
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• pp.131-138
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• 1982

Analogous to Singh's (1978) characterization of positive-Poisson distributioin and Shanmugam and Singh's (1992) characterization of logarithmic series distribution, a characterization and its statistical application of the negative binomial distribution truncated at zero are given in this paper. While it is known that under certain conditions the negative binomial distribution truncted at zero approaches the positive-Poisson and the logarithmic series distributions, we show here that the results of this paper approach in limit the results of Singh, and Shanmugam and Singh, respectively. Using the biologicla data from Sampford (1955), we illusrate our results. Also, expressions are explicitly given to test the hypothesis whether a random sample is indeed from a geometric distribution.

• Animal Systematics, Evolution and Diversity
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• v.2 no.1
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• pp.63-78
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• 1986

Two species of Moroco oxycephalus and M. lagowskii were studied to examine patterns of genic variation and morphological difference within and between populations of two species, and to clarify their taxonomic status and geographic distribution. The number of scales above lateral line(SAL) was the key character to classify these species. On the average, M.lagowskii had 22 or more SAL whereas M.oxycephalus had 20 or less. Previously known character of the position of dorsal fin was found to be not appropriate to distinguish them. Five loci, Gp, st-1, Est-2, Est-3 and Got-1 , showed fixed difference electrophoretically between two species and these could be used as genetic markers to identify them. The degree of genic variation of M. oxycephalus was four fold higher(H=0.032) than that of M. lagowskii(H=0.008) but both species were far less than the average genic variation of freshwater fish in general. Rogers' genetic similarity coefficients between two species were S=0.692 and their presumed divergent time was estimated to be sbout 1.8million years ageo. Detailed survey of the geographic distribution of thses revealed that M.lagowskii was distributed in northeastern part of South Korea(Ganseong , Gangreung, Wangsan, and Oggye) and M. oxycephalus was occupied rest of the peninsula. The distrance between Oggye, the southern limit of M. lagowskii distribution , and Samwha (near Samcheog), the northern limit of M.oxycephalus, was aobut 15 Km apart and no symparty was found in between.

• Proceedings of the Korea Concrete Institute Conference
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• 2002.05a
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• pp.393-398
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• 2002

This study shows the fatigue test results of experiment on the strengthened slabs, the probability analysis of the fatigue behavior is also presented. Static und fatigue tests were performed on bridge decks strengthened with fiber plastics(Carbon Fiber Sheet, Glass Fiber Sheet, Grid Type Carbon Fiber). In this study, to analyze the probabilistic distribution of the fatigue life, the Weibull distribution was adopted. The Weibull distribution coefficient is inferred from the S-N diagram and the number of repeated load. As the result analysis, as the stress level is higher, the fatigue limit of the strengthened bridge deck are similarly discovered but in the range of the fatigue limit, CG specimen that was strengthened with Grid Type Carbon was proved most effective of reinforcement.

• Korean Journal of Ecology and Environment
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• v.53 no.2
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• pp.195-207
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• 2020

In Korea, specific thermal elements such as annual mean temperature (AMT) 13℃, 14℃, and Kira's coldness index (CI) -10℃, have been suggested about the northernmost distribution of the warm-temperate evergreen broad-leaved forest zone. We reviewed the relationship between three thermal elements and the actual distribution of evergreen broad-leaved woody plants or its communities. Thiessen and Kriging method using point-data calibrated by seasonal lapse rate according to altitude were utilized for the spatial distribution pattern analysis. Several phytoclimatic maps were also produced in order to compare different thermal values. We identified that the AMT 13℃ was the best thermal element to demarcate the northern limit of the warm-temperate forest zone. Its area was estimated ca. 20,334 ㎢ and larger than those of other thermal elements. We concluded that an indirectly fabricated index i.e. CI -10℃ is useless and it was enough for a direct value of AMT 13℃ to represent the northern-limit distribution of warm-temperate forest zone, at least in Korea. Further researches on the reciprocity between floristic regions and phytoclimate zones are raised.

• Journal of the Korean Statistical Society
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• v.33 no.4
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• pp.449-458
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• 2004

Data envelopment analysis (DEA) estimators have been widely used in productivity analysis. The asymptotic distribution of DEA estimator derived by Kneip et al. (2003) is too complicated and abstract for analysts to use in practice, though it should be appreciated in its own right. This paper provides another way to express the limit distribution of the DEA estimator in a tractable way.

• Journal of Korean Society of Occupational and Environmental Hygiene
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• v.9 no.2
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• pp.145-157
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• 1999

Wood dust is created when machines are used to cut or shape wood materials. Industries of high risk of wood dust exposure are sawmills, dimension mills, furniture industries, and carpenters, etc. Health effects associated with wood dust exposure includes dermatitis, allergic respiratory effects and cancer. Health effects of wood dus t are mainly depend on the concentration, dust size and exposure time. This study were carried out to evaluate the concentration and particle size distribution of wood dust during working processes. The subjects of this study were 53 workers exposed to wood dust in 7 furniture factories and 5 musical instruments, and 5 sawmill factories. The average total wood dust concentrations measured by personal cascade impactor were $1.82{\pm}2.31mg/m^3$ in primary manufacture, $3.59{\pm}1.72mg/m^3$ in s econdary manufacture, $5.09{\pm}1.46mg/m^3$ in sanding operation. Mass median diameters of hardwoods dust were $3.36{\mu}m$ in primary manufacture, $4.25{\mu}m$ in secondary manufacture, $4.21{\mu}m$ in sanding operation. softwoods dust were $3.39{\mu}m$ in primary manufacture, $4.34{\mu}m$ in secondary manufacture. Particle size distributions showed a nearly the same pattern in each working processes. The sample concentration of all hardwood dust exceeded the Threshold Limit Value(TLV) and 20.8% of the softwood dust exceeded the Threshold Limit Value. The range of size distribution were $0.5-10{\mu}m$ in the soft and hardwood dust. The respirable dust of soft and hardwood took up 59% and above. Therefore new threshold limit value for wood dust should be needed in Korea. Also, it should be done for various studies on health effects related to occupational exposure of wood dust.

• Journal of Environmental Health Sciences
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• v.45 no.2
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• pp.192-202
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• 2019

Objectives: According to the central limit theorem, the samples in population might be considered to follow normal distribution if a large number of samples are available. Once we assume that toxicity dataset follow normal distribution, we can treat and process data statistically to calculate genus or species mean value with standard deviation. However, little is known and only limited studies are conducted to investigate whether toxicity dataset follows normal distribution or not. Therefore, the purpose of study is to evaluate the generally accepted normality hypothesis of aquatic toxicity dataset Methods: We selected the 8 chemicals, which consist of 4 organic and 4 inorganic chemical compounds considering data availability for the development of species sensitivity distribution. Toxicity data were collected at the US EPA ECOTOX Knowledgebase by simple search with target chemicals. Toxicity data were re-arranged to a proper format based on the endpoint and test duration, where we conducted normality test according to the Shapiro-Wilk test. Also we investigated the degree of normality by simple log transformation of toxicity data Results: Despite of the central limit theorem, only one large dataset (n>25) follow normal distribution out of 25 large dataset. By log transforming, more 7 large dataset show normality. As a result of normality test on small dataset (n<25), log transformation of toxicity value generally increases normality. Both organic and inorganic chemicals show normality growth for 26 species and 30 species, respectively. Those 56 species shows normality growth by log transformation in the taxonomic groups such as amphibian (1), crustacean (21), fish (22), insect (5), rotifer (2), and worm (5). In contrast, mollusca shows normality decrease at 1 species out of 23 that originally show normality. Conclusions: The normality of large toxicity dataset was not always satisfactory to the central limit theorem. Normality of those data could be improved through log transformation. Therefore, care should be taken when using toxicity data to induce, for example, mean value for risk assessment.

• Structural Engineering and Mechanics
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• v.62 no.3
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• pp.365-372
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• 2017

Reliability analysis is a probabilistic approach to determine a safety level of a system. Reliability is defined as a probability of a system (or a structure, in structural engineering) to functionally perform under given conditions. In the 1960s, Basler defined the reliability index as a measure to elucidate the safety level of the system, which until today is a commonly used parameter. However, the reliability index has been formulated based on the pivotal assumption which assumed that the considered limit state function is normally distributed. Nevertheless, it is not guaranteed that the limit state function of systems follow as normal distributions; therefore, there is a need to define a new reliability index for no-normal distributions. The main contribution of this paper is to define a sophisticated reliability index for limit state functions which their distributions are non-normal. To do so, the new definition of reliability index is introduced for non-normal limit state functions according to the probability functions which are calculated based on the convolution theory. Eventually, as the state of the art, this paper introduces a simplified method to calculate the reliability index for non-normal distributions. The simplified method is developed to generate non-normal limit state in terms of normal distributions using series of Gaussian functions.