• Communications for Statistical Applications and Methods
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• v.18 no.2
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• pp.219-227
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• 2011

In this paper, we proposed a generalized bivariate negative binomial distribution allowing heterogeneous dispersions on two dependent variables based on a trivariate reduction technique. In this model, we propose the score and LR tests for testing the equality of dispersions and compare the efficiencies of the proposed tests using a Monte Carlo study. The Monte Carlo study shows that the proposed score and LR tests prove to be an efficient test for the equality of dispersions in the view of the significance level and power. However, the score test is easier to compute than the LR test and it shows a slightly better performance than the LR test from the Monte Carlo study, we suggest the use of score tests for testing the equality of dispersions on two dependent variables. In addition, an empirical example is provided to illustrate the results.

• The Korean Journal of Applied Statistics
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• v.30 no.4
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• pp.579-590
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• 2017

The multivariate empirical distribution function could be defined when its distribution function can be estimated. It is known that bivariate empirical distribution functions could be visualized by using Step plot and Quantile plot. In this paper, the multivariate empirical distribution plot is proposed to represent the multivariate empirical distribution function on the unit square. Based on many kinds of empirical distribution plots corresponding to various multivariate normal distributions and other specific distributions, it is found that the empirical distribution plot also depends sensitively on its distribution function and correlation coefficients. Hence, we could suggest five goodness-of-fit test statistics. These critical values are obtained by Monte Carlo simulation. We explore that these critical values are not much different from those in text books. Therefore, we may conclude that the proposed test statistics in this work would be used with known critical values with ease.

• 한국방재학회:학술대회논문집
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• 2010.02a
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• pp.59.1-59.1
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• 2010

본 연구에서는 기존 댐을 대상으로 강우 유출 모형에 의한 과거의 홍수량 산정방식과 최근의 홍수량 산정방식을 유역 규모별로 비교하여 강우량, 강우의 시간분포, 손실분석, 기저유출 및 단위도의 매개변수 등을 변수로 홍수량 규모에 미치는 영향을 분석하였다. 분석결과 최근 계측자료를 활용하여 홍수량을 산정하는 방법이 과거의 경험식에 의한 방법과 차이를 보여 홍수량이 큰 폭으로 증가하였는데, 홍수량이 증가한 가장 큰 원인은 최근의 기상이변에 의한 강수량의 증가와 단위도의 매개변수 추정방법이 가장 큰 원인으로 분석되었다.

• Proceedings of the Korea Society for Industrial Systems Conference
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• 1999.05a
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• pp.210-216
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• 1999

In this paper, we study the estimation of system reliability for the parallel system based on Spurrier and Weier [9] bivariate Weibul distribution. We assume that when one component fails, the workload of the remaining component becomes proportional to Øλ, where Ø〉λ 0. We obtain the maximum likelihood estimators for the parameters of system reliability, and by using the numerical method, study the effects of reliability for the Parallel system.

• Journal of Korea Society of Industrial Information Systems
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• v.4 no.2
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• pp.51-56
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• 1999

In this paper, we study the estimation of system reliability for the parallel system based on Spurrier and Weier 〔9〕 bivariate Weibull distribution. We assume that when one component fails, the workload of the remaining component becomes proportional to ψλ, where ψ〉0. We obtain the maximum likelihood estimators for the parameters of system reliability, and by using the numerical method, study the effects of reliability for the parallel system.

• Tunnel and Underground Space
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• v.12 no.1
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• pp.19-30
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• 2002

Rock joint orientation is one of important geometric attributes that have an influence on the stability of rock structures such as rock slopes and tunnels. Especially, statistical models of the geometric attributes of rock joints can provide a probabilistic approach of rock engineering problems. The result from probabilistic modeling relies on the choice of statistical model. Therefore, it is critical to define a representative statistical model for joint orientation data as well as joint size and intensity and build up a series of modeling procedure including analytical validation. In this paper, we have examined a theoretical methodology for the statistical estimate and hypothesis analysis based upon Fisher distribution and bivariate normal distribution. In addition, we have proposed the algorithms of random number generator which is applied to the simulation of rock joint networks and risk analysis.

• Journal of the Korean Data and Information Science Society
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• v.7 no.2
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• pp.235-245
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• 1996

In this paper, we studied about several methods of testing hypothesis of correlation, specially Approximate method, Empirical method and Bootstrap method. The Approximate method is based on the Fisher's Z-transformation and the Empirical and Bootstrap methods approximate the distribution of the sample correlation coefficient by Monte Carlo simulation and Bootstrap technique, respectively. In order to compare how good these tests are, we computed powers under various alternatives. Consequently, we see that the Approximate test performs very well even if in small sample and all tests have almost the same power in large sample.

• Journal of Korea Water Resources Association
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• v.50 no.11
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• pp.745-758
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• 2017

The copula-based models have been successfully applied to hydrological modeling including drought frequency analysis and time series modeling. However, uncertainty estimation associated with the parameters of these model is not often properly addressed. In these context, the main purposes of this study are to develop the Bayesian inference scheme for bivariate copula functions. The main applications considered are two-fold: First, this study developed and tested an approach to copula model parameter estimation within a Bayesian framework for drought frequency analysis. The proposed modeling scheme was shown to correctly estimate model parameters and detect the underlying dependence structure of the assumed copula functions in the synthetic dataset. The model was then used to estimate the joint return period of the recent 2013~2015 drought events in the Han River watershed. The joint return period of the drought duration and drought severity was above 100 years for many of stations. The results obtained in the validation process showed that the proposed model could effectively reproduce the underlying distribution of observed extreme rainfalls as well as explicitly account for parameter uncertainty in the bivariate drought frequency analysis.

• Journal of the Korean Society of Hazard Mitigation
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• v.11 no.2
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• pp.127-136
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• 2011

In this study, annual maximum storm events are proposed to determined by the return periods considering total rainfall and rainfall intensity together. The rainfall series at Seoul since 1961 are examined and the results are as follows. First, the bivariate exponential distribution is used to determine annual maximum storm events. The parameter estimated annually provides more suitable results than the parameter estimated by whole periods. The chosen annual maximum storm events show these properties. The events with the biggest total rainfall tend to be selected in the wet years and the events with the biggest rainfall intensity in the wet years. These results satisfy the concept of critical storm events which produces the most severe runoff according to soil wetness. The average characteristics of the annual maximum storm events said average rainfall intensity 32.7 mm/hr in 1 hr storm duration(total rainfall 32.7 mm), average rainfall intensity 9.7 mm/hr in 24 hr storm duration(total rainfall 231.6 mm) and average rainfall intensity 7.4 mm/hr in 48 hr storm duration(total rainfall 355.0 mm).

• Proceedings of the Korea Water Resources Association Conference
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• 2022.05a
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• pp.200-200
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• 2022

본 연구에서는 총 강우량과 강우강도을 고려한 이변수 분석으로 연최대 호우사상을 선별하고, 두 변수를 Copula 함수로 결합하여 최적의 모델조합을 찾는 확률호우사상 산정 방법론을 제시하였다. 국내 69개 관측소의 2020년까지의 관측 자료를 대상으로 1mm 이하의 강우는 제거한 뒤, IETD(Inter-Event Time Definition) 12시간을 기준으로 강우자료를 독립적인 호우사상으로 분리하였다. 호우사상의 여러 특성 중 양의 상관관계를 갖는 총 강우량과 강우강도를 변수로 선택해 이변수 지수분포에 대입하였고, 각 지점의 연최대 호우사상 시계열을 생성하였다. 2변수 지수분포의 매개변수는 전체 기간과 연도별로 나누어 추정해 본 결과 연도별 변동성이 큰 것을 확인해 연도별 추정 방식을 선택하였다. 연최대 강우사상 시계열의 총 강우량과 강우강도는 극한 강우에 적용하는 확률분포형 중 Lognarmal, Gamma, Gumbel, GEV(Generalized Extreme Value), GPD(Generalized Pareto Distribution) 5가지를 사용하여 각각 CDF(Cumulative distribution Function) 값을 추정하였다. 계산된 CDF 값은 3가지 Copula 모형으로 결합해 joint CDF 값을 산출하였다. 총 75개의 모델조합 중 최적 모델을 찾기 위해 CVM(Cramer-von-Mises) 적합도 검정을 시행하였다. CVM의 통계량 Sn 값이 가장 작은 모델조합을 해당 지점의 최적 모델조합으로 선정하였다.