• 응용통계연구
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• 제34권5호
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• pp.735-744
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• 2021

제품의 수명을 유지시키는 것은 품질관리의 주요 목표 중 하나이다. 실제 공정에서는 시간 및 비용의 문제로 인해 모든 표본의 수명을 측정할 수 없는 경우가 많이 발생하기 때문에, 대부분 중도절단된 자료를 포함시켜 표본을 구성한다. 이 논문에서는 제1형의 우측중도절단된 수명 자료가 로그정규분포를 따르는 경우, 제품 수명의 평균을 모니터링하는 두 가지 누적합 관리도 절차를 제안한다. 하나는 우도비에 기초한 누적합 관리도이고, 다른 하나는 이항분포에 기초한 누적합 관리도 절차이다. 모의실험을 통해 평균런길이를 비교하는 방법으로 제안된 두 관리도 절차의 성능을 비교하였다. 모의실험 결과, 중도절단율이 낮은 경우, 형상모수값이 작은 경우, 평균의 감소 변화량이 큰 경우에는 우도비 누적합 관리도가 더 효율적이며, 반대로 중도절단율이 높은 경우, 형상모수값이 큰 경우, 평균의 감소 변화량이 적은 경우에는 이항 누적합 관리도가 더 효율적인 것으로 나타났다.

• 한국농공학회지
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• 제27권2호
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• pp.23-37
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• 1985

This studies were carried out to get characteristics of frequency distribution, probable flood flows according to the return periods, and the correlation between return periods and those length of records affect the Risk of failure in the annual maximum series of the main river systems in Korea. Especially, Risk analysis according to the levels were emphasized in relation to the design frequency factors for the different watersheds. Twelve watersheds along Han, Geum, Nak Dong, Yeong San and Seom Jin river basin were selected as studying basins. The results were analyzed and summarized as follows. 1. Type 1 extremal distribution was newly confirmed as a good fitted distribution at selected watersheds along Geum and Yeong San river basin. Three parameter lognormal Seom Jin river basin. Consequently, characteristics of frequency distribution for the extreme value series could be changed in connection with the watershed location even the same river system judging from the results so far obtained by author. 2. Evaluation of parameters for Type 1 extremal and three parameter lognormal distribution based on the method of moment by using an electronic computer. 3. Formulas for the probable flood flows were derived for the three parameter lognormal and Type 1 extremal distribution. 4. Equations for the risk to failure could be simplified as $\frac{n}{N+n}$ and $\frac{n}{T}$ under the condition of non-parametric method and the longer return period than the life of project, respectively. 5. Formulas for the return periods in relation to frequency factors were derived by the least square method for the three parameter lognormal and Type 1 extremal distribution. 6. The more the length of records, the lesser the risk of failure, and it was appeared that the risk of failure was increasing in propotion to the length of return periods even same length of records. 7. Empirical formulas for design frequency factors were derived from under the condition of the return periods identify with the life of Hydraulic structure in relation to the risk level. 8. Design frequency factor was appeared to be increased in propotion to the return periods while it is in inverse proportion to the levels of the risk of failure. 9. Derivation of design flood including the risk of failure could be accomplished by using of emprical formulas for the design frequency factor for each watershed.

• 대한수학회보
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• 제56권2호
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• pp.351-364
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• 2019

We derive full closed-form expressions for the prices of European symmetric power quanto call options with four different forms of terminal payoffs under the assumption of the classical lognormal asset price and exchange rate model.

• Earthquakes and Structures
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• 제5권4호
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• pp.439-459
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• 2013

Main objective of the present study is to determine the statistical properties and suitable probability distribution functions of spectral displacements from nonlinear static and nonlinear dynamic analysis within the frame work of Monte Carlo simulation for typical low rise and high rise RC framed buildings located in zone III and zone V and designed as per Indian seismic codes. Probabilistic analysis of spectral displacement is useful for strength assessment and loss estimation. To the author's knowledge, no study is reported in literature on comparison of spectral displacement including the uncertainties in capacity and demand in Indian context. In the present study, uncertainties in capacity of the building is modeled by choosing cross sectional dimensions of beams and columns, density and compressive strength of concrete, yield strength and elastic modulus of steel and, live load as random variables. Uncertainty in demand is modeled by choosing peak ground acceleration (PGA) as a random variable. Nonlinear static analysis (NSA) and nonlinear dynamic analysis (NDA) are carried out for typical low rise and high rise reinforced concrete framed buildings using IDARC 2D computer program with the random sample input parameters. Statistical properties are obtained for spectral displacements corresponding to performance point from NSA and maximum absolute roof displacement from NDA and suitable probability distribution functions viz., normal, Weibull, lognormal are examined for goodness-of-fit. From the hypothesis test for goodness-of-fit, lognormal function is found to be suitable to represent the statistical variation of spectral displacement obtained from NSA and NDA.

• 물과 미래
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• 제28권2호
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• pp.145-154
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• 1995

강우량 자료들을 수공계획에 적절히 사용하기 위해서는 강우량에 대한 다양한 해석기법이 필요하다. 본 연구에서는 연속강우량에 따른 강우사상계열의 수문빈도해석을 위한 확률분포를 연구한 것이다. 2변량 정규분포, 2변량 대수정규분포, 2변량 gamma 분포가 강릉, 서울, 인천, 추풍령, 대구, 전주, 광주, 부산지점의 연속최대 강우량과 그 지속기간으로 이루어진 강우사상의 확률분포로서 적용되었다. 이들 지점의 강우사상 자료가 2변량 정규분포, 2변량 대수정규분포에는 적합되었으나 2변량 gamma 분포에는 적합되지 않았다. 적합도 검정을 통하여 선정된 최적 분포형으로부터 확률강우사상의 빈도곡선을 제시하였다.

• Earthquakes and Structures
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• 제12권2호
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• pp.153-163
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• 2017

The underlying goal of the present paper is to investigate soil and structural uncertainties on impedance functions and structural response of soil-shallow foundation-structure (SSFS) system using Monte Carlo simulations. The impedance functions of a rigid massless circular foundation resting on the surface of a random soil layer underlain by a homogeneous half-space are obtained using 1-D wave propagation in cones with reflection and refraction occurring at the layer-basement interface and free surface. Firstly, two distribution functions (lognormal and gamma) were used to generate random numbers of soil parameters (layer's thickness and shear wave velocity) for both horizontal and rocking modes of vibration with coefficients of variation ranging between 5 and 20%, for each distribution and each parameter. Secondly, the influence of uncertainties of soil parameters (layer's thickness, and shear wave velocity), as well as structural parameters (height of the superstructure, and radius of the foundation) on the response of the coupled system using lognormal distribution was investigated. This study illustrated that uncertainties on soil and structure properties, especially shear wave velocity and thickness of the layer, height of the structure and the foundation radius significantly affect the impedance functions, and in same time the response of the coupled system.

• 대한교통학회지
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• 제26권5호
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• pp.217-226
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• 2008

통행시간 신뢰성은 통행자가 예측하기 힘든 통행시간의 변동을 설명하는 개념이다. 본 연구는 통행시간 신뢰성을 측정할 수 있는 지표를 개발하고, 국내 도로 및 철도 이용 실적자료를 바탕으로 통행시간 신뢰성 지표 원단위를 산정한다. 통행시간 신뢰성 측정 지표로 수정형 완충시간 지표를 제안하며, 신뢰성/비신뢰성의 임계점으로는 로그정규 통행시간분포를 기반으로 한 계획 통행시간과 실제 통행시간의 차이를 측정한다. 이를 통해 철도는 상수형 도로는 음의 포물선형 통행시간 신뢰성 지표함수를 개발한다. 본 연구의 결과가 도로 및 철도 투자사업의 신중한 의사결정에 일조할 수 있기를 기대한다.

• 응용통계연구
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• 제23권2호
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• pp.325-333
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• 2010

Protection against disclosure of survey respondents' identifiable and/or sensitive information is a prerequisite for statistical agencies that release microdata files from their sample surveys. Coarsening is one of popular methods for protecting the confidentiality of the data. Grouped data can be released in the form of microdata or tabular data. Instead of releasing the data in a tabular form only, having microdata available to the public with interval codes with their representative values greatly enhances the utility of the data. It allows the researchers to compute covariance between the variables and build statistical models or to run a variety of statistical tests on the data. It may be conjectured that the variance of the interval data is lower that of the ungrouped data in the sense that the coarsened data do not have the within interval variance. This conjecture will be investigated using the uniform and triangular distributions. Traditionally, midpoint is used to represent all the values in an interval. This approach implicitly assumes that the data is uniformly distributed within each interval. However, this assumption may not hold, especially in the last interval of the economic data. In this paper, we will use three distributional assumptions - uniform, Pareto and lognormal distribution - in the last interval and use either midpoint or median for other intervals for wage and food costs of the Statistics Korea's 2006 Household Income and Expenditure Survey(HIES) data and compare these approaches in terms of the first two moments.

• 천문학회보
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• 제35권2호
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• pp.75.1-75.1
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• 2010

The nature and origin of the intergalactic magnetic field (IGMF) are an outstanding problem of cosmology, yet they are not well understood. Measuring Faraday rotation (RM) is one of a few promising methods to explore the IGMF. We have theoretically investigated RM using a model of the IGMF based on a MHD turbulence dynamo (Ryu et al. 2008; Cho et al. 2009). In the previous KAS meeting, we reported the results for the present-day local universe; for instance, the probability distribution function (PDF) of ${\mid}RM{\mid}$ follows the lognormal distribution, the root mean square (rms) value for filaments is ~1 rad m^{-2}, and the power spectrum peaks at ~1 h^{-1} Mpc scale. In this talk, we extend our study of RM; by stacking simulation data up to redshift z=5 and taking account of the redshift distribution of radio sources, we have reproduced an observable view of RM through filaments against background radio sources. Our findings are as follows. The inducement of RM is a random walk process, so that the rms of RM increases with increasing path length. The rms value of RM for filaments reaches several rad m^{-2}. The PDF still follows the lognormal distribution, and the power spectrum of RM peaks at less than degree scale. Our predictions of RM could be tested, for instance, with LOFAR, ASKAP, MEERKAT, and SKA.

• Communications for Statistical Applications and Methods
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• 제19권6호
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• pp.837-847
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• 2012

Inverse Gaussian distribution is widely used in applications to analyze and model right-skewed data. To assess the appropriateness of the distribution prior to data analysis, Mudholkar and Tian (2002) proposed an entropy-based test of fit. The test is based on the entropy power fraction(EPF) index suggested by Gokhale (1983). The simulation results report that the power of the entropy-based test is superior compared to other goodness-of-fit tests; however, this observation is based on the small-scale simulation results on the standard exponential, Weibull W(1; 2) and lognormal LN(0:5; 1) distributions. A large-scale simulation should be performed against various alternative distributions to evaluate the power of the entropy-based test; however, the use of a theoretical method is more effective to investigate the powers. In this paper, utilizing the information discrimination(ID) index defined by Ehsan et al. (1995) as a mathematical tool, we scrutinize the power of the entropy-based test. The selected alternative distributions are the gamma, Weibull and lognormal distributions, which are widely used in data analysis as an alternative to inverse Gaussian distribution. The study results are provided and an illustrative example is analyzed.