• Communications for Statistical Applications and Methods
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• v.20 no.3
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• pp.169-174
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• 2013

The ROC curve is drawn with two conditional cumulative distribution functions (or survival functions) of the univariate random variable. In this work, we consider joint cumulative distribution functions of k random variables, and suggest a ROC curve for multivariate random variables. With regard to the values on the line, which passes through two mean vectors of dichotomous states, a joint cumulative distribution function can be regarded as a function of the univariate variable. After this function is modified to satisfy the properties of the cumulative distribution function, a ROC curve might be derived; moreover, some illustrative examples are demonstrated.

• International Journal of Reliability and Applications
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• v.18 no.2
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• pp.65-82
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• 2017

Abstract. Camilo Dagum proposed several variants of a new model for the size distribution of personal income in a series of papers in the 1970s. He traced the genesis of the Dagum distributions in applied economics and points out parallel developments in several branches of the applied statistics literature. The main aim of this paper is to define a bivariate Dagum distribution so that the marginals have Dagum distributions. It is observed that the joint probability density function and the joint cumulative distribution function can be expressed in closed forms. Several properties of this distribution such as marginals, conditional distributions and product moments have been discussed. The maximum likelihood estimates for the unknown parameters of this distribution and their approximate variance-covariance matrix have been obtained. Some simulations have been performed to see the performances of the MLEs. One data analysis has been performed for illustrative purpose.

• Journal of the Korean Institute of Navigation
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• v.11 no.1
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• pp.67-91
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• 1987

In this paper, a synthetic method for evaluating the seakeeping performance of a ship in waves is studied. For the prediction and evaluation of irregular phenomena to be correlated each other, the multi-dimensional Rayleigh's joint probability density function and the cumulative distribution function are approximated. According to this approximated function, it is able to calculate easily the occurrence probability of the factors on seakeeping performance. We proposed an evaluation method and an index to be defined by the seakeeping performance reliability, that is considered as the dangerousness and the relative dangerousness of the factors on seakeeping performance in waves. The use of this method aid index will be effective to install the sensors which are necessary to evaluate the states of ships at sea. Some example of the calculations by this method for 175m length single screw container ship equipped with diesel engine are also presented.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.15 no.5
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• pp.2603-2609
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• 2014

Reliability analysis of mechanical systems requires statistical modeling of input random variables such as distribution function types and statistical parameters that affect the performance of the mechanical systems. Some random variables are correlated, but considered as independent variables or wrong assumptions on input random variables have been used. In this paper, joint distributions were modeled using copulas and Bayesian method from limited number of data. To verify the proposed method, statistical simulation tests were carried out for various number of samples and correlation coefficients. As a result, the Bayesian method selected the most probable copula types among candidate copulas even though the candidate copula shapes are similar for low correlations or the number of data is limited. The most probable copulas also yielded similar reliabilities with the true reliability obtained from a true copula, so that it can be concluded that the Bayesian method provides accurate statistical modeling for the reliability analysis.

• Fire Science and Engineering
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• v.20 no.1 s.61
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• pp.6-14
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• 2006

The data of city gas accidents has been collected and analysed for not only predictions of the fire and explosion accidents but also the criteria of societal risk. The accidents of the recent 11 years have been broken up into such 3 groups roughly as "release", "explosion", "fire" d 16 groups in detail. Owing to the Poisson probability distribution functions, 'careless work-explosion-pipeline' and 'joint loosening & erosion-release-pipeline' items respectively have turned out to record the lowest and most frequency among the recent 11-years accidents. And thus the proper counteractions must be carried out. In order to assess the societal risks tendency of the fatal gas accidents and set the more obvious safety policies up, the D. O. Hogon equation and the regression method has been used to range the acceptable range in the F-N curve of the cumulative casualties. The further works requires setting up successive database on the fire and explosion accidents systematically to obtain reliable analyses. Also the standard codification will be demanded.

• 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.

• Communications for Statistical Applications and Methods
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• v.19 no.2
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• pp.277-286
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• 2012

For credit assessment models, the ROC curves evaluate the classification performance using two univariate cumulative distribution functions of the false positive rate and true positive rate. In this paper, it is extended to two bivariate normal distribution functions of default and non-default borrowers; in addition, the bivariate ROC curves are proposed to represent the joint cumulative distribution functions by making use of the linear function that passes though the mean vectors of two score random variables. We explore the classification performance based on these ROC curves obtained from various bivariate normal distributions, and analyze with the corresponding AUROC. The optimal threshold could be derived from the bivariate ROC curve using many well known classification criteria and it is possible to establish an optimal cut-off criteria of bivariate mixture distribution functions.

• Journal of the Society of Naval Architects of Korea
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• v.51 no.3
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• pp.193-202
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• 2014

This paper presents a new method of sampling the climatic data for infrared signature analysis. Historical hourly data from a stationary marine buoy of KMA(Korean Meteorological Administration) are used to select a small number of sample points (N=100) to adequately cover the range of statistics(PDF, CDF) displayed by the original data set (S=56,670). The method uses a coarse bin to subdivide the variable space ($3^5$=243 bins) to make sample points cover the original data range, and a single-point ranking system to select individual points so that uniform coverage (1/N = 0.01) is obtained for each variable. The principal component analysis is used to calculate a joint probability of the coupled climatic variables. The selected sample data show good agreement to the original data set in statistical distribution and they will be used for statistical analysis of infrared signature and susceptibility of naval ships.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.4
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• pp.1866-1883
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• 2019

As the youngest branch of information hiding, network covert timing channels conceal the existence of secret messages by manipulating the timing information of the overt traffic. The popular model-based framework for constructing covert timing channels always utilizes cumulative distribution function (CDF) of the inter-packet delays (IPDs) to modulate secret messages, whereas discards high-order statistics of the IPDs completely. The consequence is the vulnerability to high-order statistical tests, e.g., entropy test. In this study, a rich security model of covert timing channels is established based on IPD chains, which can be used to measure the distortion of multi-order timing statistics of a covert timing channel. To achieve rich security, we propose two types of covert timing channels based on nested lattices. The CDF of the IPDs is used to construct dot-lattice and interval-lattice for quantization, which can ensure the cell density of the lattice consistent with the joint distribution of the IPDs. Furthermore, compensative quantization and guard band strategy are employed to eliminate the regularity and enhance the robustness, respectively. Experimental results on real traffic show that the proposed schemes are rich-secure, and robust to channel interference, whereas some state-of-the-art covert timing channels cannot evade detection under the rich security model.

• Journal of the Korean Institute of Gas
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• v.10 no.1 s.30
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• pp.48-55
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• 2006

In order to establish the comprehensively, quantitatively predictable program to the fire and explosion accidents in the urban gas system, and to set up domestic criteria of societal risk, the collected urban gas accident data have been deeply analyzed. The Poisson probability distribution functions with t=5 for the database of the gas accidents in recent 11 year shows that 'careless work-explosion-pipeline' item has the lowest frequency, whereas 'joint loosening & erosion-release-pipeline' item has the highest frequency. And thus the proper counteractions must be carried out. The further works requires setting up successive database on the fire and explosion accidents systematically to obtain reliable analyses.