• Title/Summary/Keyword: joint conditional distribution

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A Bayesian Approach to Linear Calibration Design Problem

  • Kim, Sung-Chul
    • Journal of the Korean Operations Research and Management Science Society
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    • v.20 no.3
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    • pp.105-122
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    • 1995
  • Based on linear models, the inference about the true measurement x$_{f}$ and the optimal designs x (nx1) for the calibration experiments are considered via Baysian statistical decision analysis. The posterior distribution of x$_{f}$ given the observation y$_{f}$ (qxl) and the calibration experiment is obtained with normal priors for x$_{f}$ and for themodel parameters (.alpha., .betha.). This posterior distribution is not in the form of any known distributions, which leads to the use of a numerical integration or an approximation for the calculation of the overall expected loss. The general structure of the expected loss function is characterized in the form of a conjecture. A near-optimal design is obtained through the approximation nof the conditional covariance matrix of the joint distribution of (x$_{f}$ , y$_{f}$ $^{T}$ )$^{T}$ . Numerical results for the univariate case are given to demonstrate the conjecture and to evaluate the approximation.n.

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Influence of Joint Distribution of Wave Heights and Periods on Reliability Analysis of Wave Run-up (처오름의 신뢰성 해석에 대한 파고_주기결합분포의 영향)

  • Lee Cheol-Eung
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.17 no.3
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    • pp.178-187
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    • 2005
  • A reliability analysis model f3r studying the influence of joint distribution of wave heights and periods on wave un-up is presented in this paper. From the definition of failure mode related to wave run-up, a reliability function may be formulated which can be considered uncertainties of water level. In particular, the reliability analysis model can be directly taken into account statistical properties and distributions of wave periods by considering wave period in the reliability function to be a random variable. Also, variations of wave height distribution conditioned to mean wave periods can be taken into account correctly. By comparison of results of additional reliability analysis using extreme distributions with those resulted from joint distribution of wave height and periods, it is found that probabilities of failure evaluated by the latter is larger than those by the former. Although the freeboard of sloped-breakwater structures can be determined by extreme distribution based on the long-term measurements, it may be necessary to investigate additionally into wave run-up by using the present reliability analysis model formulated to consider joint distribution of a single storm event. In addition, it may be found that the effect of spectral bandwidth parameter on reliability index may be little, but the effect of wave height distribution conditioned to mean wave periods is straightforward. Therefore, it may be confirmed that effects of wave periods on the probability of failure of wave run-up may be taken into account through the conditional distribution of wave heights. Finally, the probabilities of failure with respect to freeboard of sloped-breakwater structures can be estimated by which the rational determination of crest level of sloped-breakwater structures may be possible.

The Characteristics of Wave Statistical Data and Quality Assurance (파랑 통계자료의 특성과 신뢰성 검토)

  • Park, J.H.
    • Journal of Power System Engineering
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    • v.13 no.2
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    • pp.63-70
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    • 2009
  • This paper discusses the influence on long-tenn predictions of the ship response in ocean by using the Global Wave Statistics data, GWS, and wave information from the remote sensing satellites. GWS's standard scatter diagrams of significant wave height and zero-crossing wave period are suggested to be corrected to a round number of 0.01/1000 fitted with a statistical analytic model of the conditional lognormal distribution for zero-crossing wave period. The GEOSAT satellite data are utilized which presented by I. R. Young and G. J. Holland (1996, named as GEOSAT data). At first, qualities of this data are investigated, and statistical characteristic trends are studied by means of applying known probability distribution functions. The wave height data of GEOSAT are compared to the data observed onboard merchant ships, the data observed by measure instrument installed on the ocean-going container ship and so on. To execute a long-tenn prediction of ship response, joint probability functions between wave height and wave period are introduced, therefore long-term statistical predictions are executed by using the functions.

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Review of Screening Procedure as Statistical Hypothesis Testing (통계적 가설검정으로서의 선별검사절차의 검토)

  • 권혁무;이민구;김상부;홍성훈
    • Journal of Korean Society for Quality Management
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    • v.26 no.2
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    • pp.39-50
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    • 1998
  • A screening procedure, where one or more correlated variables are used for screeing, is reviewed from the point of statistical hypothesis testing. Without assuming a specific probability model for the joint distribution of the performance and screening variables, some principles are provided to establish the best screeing region. A, pp.ication examples are provided for two cases; ⅰ) the case where the performance variable is dichotomous and ⅱ) the case where the performance variable is continuous. In case ⅰ), a normal model is assumed for the conditional distribution of the screening variable given the performance variable. In case ⅱ), the performance and screening variables are assumed to be jointly normally distributed.

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Probable annual maximum of daily snowfall using improved probability distribution (개선된 확률밀도함수 적용을 통한 빈도별 적설심 산정)

  • Park, Heeseong;Chung, Gunhui
    • Journal of Korea Water Resources Association
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    • v.53 no.4
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    • pp.259-271
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    • 2020
  • In Korea, snow damage has happened in the region with little snowfalls in history. Also, accidental damage was caused by heavy snow leads and the public interest on heavy snow has been increased. Therefore, policy about the Natural Disaster Reduction Comprehensive Plan has been changed to include the mitigation measures of snow damage. However, since heavy snow damage was not frequent, studies on snowfall have not been conducted on different points. The characteristics of snow data commonly are not the same as the rainfall data. Some southern coastal areas in Korea are snowless during the year. Therefore, a joint probability distribution was suggested to analyze the snow data with many 0s in a previous research and fitness from the joint probability distribution was higher than the conventional methods. In this study, snow frequency analysis was implemented using the joint probability distribution and compared to the design codes. The results were compared to the design codes. The results of this study can be used as the basic data to develop a procedure for the snow frequency analysis in the future.

Method for Evaluating Optimal Air Monitoring Sites for SO2 in Ulsan (울산광역시 아황산가스(SO2)의 최적관측소 평가방법)

  • Lim, Junghyun;Yoon, Sanghoo
    • Journal of Environmental Science International
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    • v.26 no.9
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    • pp.1073-1080
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    • 2017
  • Manufacturing and technology industries produce large amounts of air pollutants. Ulsan Metropolitan City, South Korea, is well-known for its large industrial complexes; in particular, the concentration of $SO_2$ here is the highest in the country. We assessed $SO_2$ monitoring sites based on conditional and joint entropy, because this is a common method for determining an optimal air monitoring network. Monthly $SO_2$ concentrations from 12 air monitoring sites were collected, and the distribution of spatial locations was determined by kriging. Mean absolute error, Root Mean Squared Error (RMSE), bias and correlation coefficients were employed to evaluate the considered algorithms. An optimal air monitoring network for Ulsan was suggested based on the improvement of RMSE.

Derived I-D-F Curve in Seoul Using Bivariate Precipitation Frequency Analysis (이변량 강우 빈도해석을 이용한 서울지역 I-D-F 곡선 유도)

  • Kwon, Young-Moon;Kim, Tae-Woong
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.29 no.2B
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    • pp.155-162
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    • 2009
  • Univariate frequency analyses are widely used in practical hydrologic design. However, a storm event is usually characterized by amount, intensity, and duration of the storm. To fully understand these characteristics and to use them appropriately in hydrologic design, a multivariate statistical approach is necessary. This study applied a Gumbel mixed model to a bivariate storm frequency analysis using hourly rainfall data collected for 46 years at the Seoul rainfall gauge station in Korea. This study estimated bivariate return periods of a storm such as joint return periods and conditional return periods based on the estimation of joint cumulative distribution functions of storm characteristics. These information on statistical behaviors of a storm can be of great usefulness in the analysis and assessment of the risk associated with hydrologic design problems.

Frequency analysis for annual maximum of daily snow accumulations using conditional joint probability distribution (적설 자료의 빈도해석을 위한 확률밀도함수 개선 연구)

  • Park, Heeseong;Chung, Gunhui
    • Journal of Korea Water Resources Association
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    • v.52 no.9
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    • pp.627-635
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    • 2019
  • In Korea, snow damage has been happened in the region with no snowfalls in history. Also, casual damage was caused by heavy snow. Therefore, policy about the Natural Disaster Reduction Comprehensive Plan has been changed to include the mitigation measures of snow damage. However, since heavy snow damage was not frequent, studies on snowfall have not been conducted in different points. The characteristics of snow data commonly are not same to the rainfall data. For example, some parts of the southern coastal areas are snowless during the year, so there is often no values or zero values among the annual maximum daily snow accumulation. The characteristics of this type of data is similar to the censored data. Indeed, Busan observation sites have more than 36% of no data or zero data. Despite of the different characteristics, the frequency analysis for snow data has been implemented according to the procedures for rainfall data. The frequency analysis could be implemented in both way to include the zero data or exclude the zero data. The fitness of both results would not be high enough to represent the real data shape. Therefore, in this study, a methodology for selecting a probability density function was suggested considering the characteristics of snow data in Korea. A method to select probability density function using conditional joint probability distribution was proposed. As a result, fitness from the proposed method was higher than the conventional methods. This shows that the conventional methods (includes 0 or excludes 0) overestimated snow depth. The results of this study can affect the design standards of buildings and also contribute to the establishment of measures to reduce snow damage.

Study on Teachers' Understanding on Generating Random Number in Monte Carlo Simulation (몬테카를로 시뮬레이션의 난수 생성에 관한 교사들의 이해에 관한 연구)

  • Heo, Nam Gu;Kang, Hyangim
    • School Mathematics
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    • v.17 no.2
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    • pp.241-255
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    • 2015
  • The purpose of this study is to analyze teachers' understanding on generating random number in Monte Carlo simulation and to provide educational implications in school practice. The results showed that the 70% of the teachers selected wrong ideas from three types for random-number as strategies for problem solving a probability problem and also they make some errors to justify their opinion. The first kind of the errors was that the probability of a point or boundary was equal to the value of the probability density function in the continuous probability distribution. The second kind of the errors was that the teachers failed to recognize that the sample space has been changed by conditional probability. The third kind of the errors was that when two random variables X, Y are independence of each other, then only, joint probability distribution is satisfied $P(X=x,\;Y=y)=p(X=x){\times}P(Y=y{\mid}X=x)$.

Bivariate reliability models with multiple dynamic competing risks (다중 동적 Competing Risks 모형을 갖는 이변량 신뢰성 모형에 관한 연구)

  • Kim, Juyoung;Cha, Ji Hwan
    • Journal of the Korean Data and Information Science Society
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    • v.27 no.3
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    • pp.711-724
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    • 2016
  • Under variable complex operating environment, various factors can affect the lifetimes of systems. In this research, we study bivariate reliability models having multiple dynamic competing risks. As competing risks, in addition to the natural failure, we consider the increased stress caused by the failure of one component, external shocks, and the level of stress of the working environment at the same time. Considering two reliability models which take into account all of these competing risks, we derive bivariate life distributions. Furthermore, we compare these two models and also compare the distributions of maximum and minimum statistics in the two models.