• 물과 미래
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• 제7권2호
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• pp.107-111
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• 1974

Annual runoff in the Nakdong river basin has been analyzed to find the probability functions of best fit to distribution of historical annual runoff. The results obtained are as follows; (1) Log-normal 3-parameter disrtibution is believed as the probability function of best fit to historical distribution (2) Log-normal 3-parameter disrtibution is believed as the best fit probability function among Log-normal dist-ributions. (3) In the test of goodness of fit, $x^2-test$ shows that probability of $x^2-valus$ in Log-normal 3-parameter distribution is nearly more than 90%. But in the Simirnov-Kolmogorov test, hypotheses for the probability distributions cannot be rejected at significance level 5% & 1%. (4) Among 7 gauging stations, Dongchon & Koryung-Bridge's records show lower fitness to the theoretical probability functions than other 5 gauging station's

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2020년도 학술발표회
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• pp.362-362
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• 2020

Flash flood is a dangerous weather phenomenon, affecting humans and the economy. The identification, forecast of the changing trend and its characteristics are increasingly concerned. In the world, there have many methods for determining the characteristics of flash floods, in which flash flood guidance (FFG) is a fast, effective and widely used method. The main source of flash floods is short-term rainfall. In this study, we used the data of cross-sectional measurement at the tributaries and the hourly rain data from the automatic rainfall measurement stations in the Geum river basin. Besides, we use a combination of the flash flood guidance and the best fit distribution function to estimate the repeatability of flash floods for head-water catchments in Geum river basin. In which, FFG determines the threshold of rainfall for flash floods. The study has determined the best hourly rainfall distribution function for the Geum river basin and estimated the maximum rainfall of 1hr according to the return periods.

• 물과 미래
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• 제8권1호
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• pp.80-88
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• 1975

In this paper the authors established the best fit distribution function by applying the concept of probabiaity to the annual minimum flow of nine areas along the Nakdong river basin which is one of the largest Korean rivers and calculated the probable minimum flow suitable to those distribution function. Lastly, the authors tried to establish the best method to estimate the probable minimun flow by comparing some frequency analysis methods. The results obtained are as follows (1) It was considered that the extremal distribution type III was the most suitable one in the distributional types as a result of the comparision with Exponential distribution, Log-Normal distribution, Extremal distribution type-III and so on. (2) It was found that the formula of extremal distribution type-II for the estimation of probable minimum flow gave the best result in deciding the probable minimum flow of the Nakdong river basin. Therfore, it is recommended that the probable minimum flow should be estimated by using the extremal distribution type-III method. (3) It could be understood that in the probable minimum flow the average non-excessive probability appeared to be $Po{\fallingdotseq}1-\frac{1}{2T}$ and gave the same values of the probable variable without any difference in the various methods of plotting technique.

• 물과 미래
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• 제7권2호
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• pp.99-106
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• 1974

The records of wave heights which were observed at Muk ho and Po hang of the East Coast of Korea were analized by several probility functions. The exponential 2 parameter distribution was found as the best fit probability function to the historical distribution of wave heights by the test of goodness of fit. But log-normal 2 parameter and log-extremal type A distributions were also fit to the historical distribution, especially in the Smirnov-Kolmogorov test. Therefore, it can't be always regarded that those two distributions are not fit to the wave heiht's distribution. In the test of goodness of fit, the Chi-Square test gave very sensitive results and Smirnov-Kolmogorov test, which is a distribution free and non-parametric test, gave more inclusive results. At the next stage, the inter-relationship between the mean and the one-third wave heights, the mean and the one-=tenth wave heights, the one-third and the one-tenth wave heights, the one-third and the highest wave heights were obtained and discussed.

• 천문학회보
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• 제40권2호
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• pp.38.3-38.3
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• 2015

Recently, the Pierre Auger Observatory (PAO), the largest ground-based project for detecting ultra-high-energy cosmic rays (UHECRs), published their 10-year data. We can access an unprecedented number of UHECR data observed by the project, which give us a possibility to get an accurate statistical test result. In this work, we investigate the influence of the galactic magnetic field (GMF) on the distribution of UHECRs by searching the correlation with the large-scale structure (LSS) of the universe. We simulate the mock UHECR events whose trajectories from the sources would be deflected by the Gaussian smearing angle which reflects the influence by the GMF. By the statistical test, we compare the correlation between the expected/observed distribution of UHECRs and the LSS of the universe in the regions of sky divided by the galactic latitude, varying the smearing angle. Here, we assume the deflections by the GMF are mainly dependent on the galactic latitude. Using the maximum likelihood estimation, we find the best-fit smearing angle in each region. If we get a trend that best-fit smearing angles differ from each region, the influence of GMF may be stronger than that of intergalactic magnetic fields (IGMF) because it is known that the distribution of IGMF follows the LSS of the universe. Also, we can estimate the strength of the GMF using the best-fit parameter by the maximum likelihood.

• Asian Pacific Journal of Cancer Prevention
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• 제17권12호
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• pp.5287-5294
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• 2016

Background: Breast cancer is a worldwide public health concern and is the most prevalent type of cancer in women in the United States. This study concerned the best fit of statistical probability models on the basis of survival times for nine state cancer registries: California, Connecticut, Georgia, Hawaii, Iowa, Michigan, New Mexico, Utah, and Washington. Materials and Methods: A probability random sampling method was applied to select and extract records of 2,000 breast cancer patients from the Surveillance Epidemiology and End Results (SEER) database for each of the nine state cancer registries used in this study. EasyFit software was utilized to identify the best probability models by using goodness of fit tests, and to estimate parameters for various statistical probability distributions that fit survival data. Results: Statistical analysis for the summary of statistics is reported for each of the states for the years 1973 to 2012. Kolmogorov-Smirnov, Anderson-Darling, and Chi-squared goodness of fit test values were used for survival data, the highest values of goodness of fit statistics being considered indicative of the best fit survival model for each state. Conclusions: It was found that California, Connecticut, Georgia, Iowa, New Mexico, and Washington followed the Burr probability distribution, while the Dagum probability distribution gave the best fit for Michigan and Utah, and Hawaii followed the Gamma probability distribution. These findings highlight differences between states through selected sociodemographic variables and also demonstrate probability modeling differences in breast cancer survival times. The results of this study can be used to guide healthcare providers and researchers for further investigations into social and environmental factors in order to reduce the occurrence of and mortality due to breast cancer.

• 한국항해항만학회지
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• 제37권5호
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• pp.453-461
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• 2013

본 논문에서는 소형 해상 부유체의 위기 평가를 위한 확률기반 위기평가기법(PET)에서 표본 데이터에 최적인 누적분포함수(CDF) 추정에 관한 평가절차와 실험결과를 기술하였다. CDF는 PET에서 부유체의 위기수준을 평가하기 위한 위기허용기준의 참조 값을 제공하기 위한 것으로, 부유체 모델의 롤(Roll), 피치(pitch), 히브(Heave) 등의 운동응답함수에 대한 표본 데이터에서 추정할 수 있다. 본 연구에서는 여덟가지 정형화된 분포함수와 최대우도추정기법을 적용하여 표본 데이터에 대해서 최대우도를 갖는 CDF들을 평가하였다. 분포함수들의 적합도 검정 실험을 통해서, 베타 분포가 롤과 피치 표본 데이터에 대해서 평균 확률오차 $\bar{\delta}(0{\leq}\bar{\delta}{\leq}1.0)$가 가장 작은 0.024와 0.022로 최적임을 나타냈고, 히브 표본 데이터에 대해서는 감마 분포가 $\bar{\delta}$가 가장 작은 0.027로 최적임을 나타냈다. 본 연구에서 제안한 방법은 표본 데이터의 최적분포 추정을 위한 다양한 분야에 적용 가능할 것으로 기대된다.

• 한국농공학회지
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• 제21권4호
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• pp.108-117
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• 1979

In order to obtain the basic data for design of water structures which can be contributed to the planning of water use. Best fitted distribution function and the equations for the probable minimum flow were derived to the annual minimum flow of five subwatersheds along Geum River basin. The result were analyzed and summarized as follows. 1. Type III extremal distribution was considered as a best fit one among some other distributions such as exponential and two parameter lognormal distribution by $x^2$-goodness of fit test. 2. The minimum flow are analyzed by Type III extremal distribution which contains a shape parameter $\lambda$, a location parameter ${\beta}$ and a minimum drought $\gamma$. If a minimum drought $\gamma=0$, equations for the probable minimum flow, $D_T$, were derived as $D_T={\beta}e^{\lambda}1^{y'}$, with two parameters and as $D_T=\gamma+(\^{\beta}-\gamma)e^{{\lambda}y'}$ with three parameters in case of a minimum drought ${\gamma}>0$ respectively. 3. Probable minimum flow following the return periods for each stations were also obtained by above mentioned equations. Frequency curves for each station are drawn in the text. 4. Mathematical equation with three parameters is more suitable one than that of two parameters if much difference exist between the maximum and the minimum value among observed data.

• Geomechanics and Engineering
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• 제35권5호
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• pp.499-509
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• 2023

The objective of this study is to perform outlier analysis to obtain the distribution of groundwater levels through the best model. The groundwater levels are measured in 10, 25 and 30 piezometers in Seoul, Daejeon and Suncheon in South Korea. Fifty-eight empirical distribution functions were applied to determine a suitable fit for the measured groundwater levels. The best fitted models based on the measured values are determined as the Generalized Pareto distribution, the Johnson SB distribution and the Normal distribution for Seoul, Daejeon and Suncheon, respectively; the reliability is estimated through the Anderson-Darling method. In this study, to choose the appropriate confidence interval, the relationship between the amount of outlier data and the confidence level is demonstrated, and then the 95% is selected at a reasonable confidence level. The best model shows a smaller error ratio than the GEV while the Mahalanobis distance and outlier labelling methods results are compared and validated. The outlier labelling and Mahalanobis distance based on median shown higher validated error ratios compared to their mean equivalent suggesting, the methods sensitivity to data structure.

• 국제학술발표논문집
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• The 4th International Conference on Construction Engineering and Project Management Organized by the University of New South Wales
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• pp.395-398
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• 2011

This paper introduces stochastic cash-flow modeling integrated with simulation based scheduling. The system makes use of CPM schedule data exported from commercial scheduling software, computes the best fit probability distribution functions (PDFs) of historical activity durations, assigns the PDFs identified to respective activities, simulates the schedule network, computes the deterministic and stochastic project cash-flows, plots the corresponding cash flow diagrams, and estimates the best fit PDFs of overdraft and net profit of a project. It analyzes the effect of different distributions of activity durations on the distribution of overdrafts and net profits, and improves reliability compared to deterministic cash flow analysis.