• Ocean Systems Engineering
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• v.12 no.3
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• pp.267-284
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• 2022

A subsea pipeline designed across active shipping lane prones to failure against external interferences such as anchorage activities, hence risk assessment is essential. It requires quantifying the geometric probability derived from ship traffic distribution based on Automatic Identification System (AIS) data. The actual probability density function from historical vessel traffic data is ideal, as for rapid assessment, conceptual study, when the AIS data is scarce or when the local vessels traffic are not utilised with AIS. Recommended practices suggest the probability distribution is assumed as a single peak Gaussian. This study compares several fitted Gaussian distributions and Monte Carlo simulation based on actual ship traffic data in main ship direction in an active shipping lane across a subsea pipeline. The results shows that a Gaussian distribution with five peaks is required to represent the ship traffic data, providing an error of 0.23%, while a single peak Gaussian distribution and the Monte Carlo simulation with one hundred million realisation provide an error of 1.32% and 0.79% respectively. Thus, it can be concluded that the multi-peak Gaussian distribution can represent the actual ship traffic distribution in the main direction, but it is less representative for ship traffic distribution in other direction. The geometric probability is utilised in a quantitative risk assessment (QRA) for subsea pipeline against vessel anchor dropping and dragging and vessel sinking.

• Journal of Korean Society of Transportation
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• v.23 no.5 s.83
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• pp.113-120
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• 2005

Highway geometric design aims to provide drivers with safe and efficient road conditions. Highway design method of Korea doesn't consider demand characteristics of drivers, vehicles etc. Therefore there is a gap between designer's expectation and user's behavior and it hinders to make safer roads. It is required to develop the geometric design criteria and design method based on driving characteristics to provide safe and flexible design. This study suggested a geometric design method of horizontal curves on rural 4-lane highways based on speed distribution.

• Communications for Statistical Applications and Methods
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• v.6 no.2
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• pp.595-600
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• 1999

We present a simple geometric approach which uses polar transformation and elementary trigonometry to evaluating an orthant probability in a bivariate normal distribution. Figures are provided to illustrate the situation for varying correlation coefficient. We derive the distribution of the sample correlation coefficient from a bivariate normal distribution when the sample size is 2 as an application.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.505-511
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• 2007

In this paper, we examine the Markov chain $\{X_k,\;N_k;\;k=0,\;1,...$. We show that the marginal steady state distribution of Xk is discrete phase type. The implication of this result is that the queue length distribution of phase type for large number of examples where this Markov chain is applicable and shows a queueing application by matrix geometric methods.

• Journal of the Korean Data and Information Science Society
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• v.21 no.6
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• pp.1109-1115
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• 2010

In this paper, exact confidence interval of hyper-geometric parameter, that is the probability of success p in the population is discussed. Usually, binomial distribution is a well known discrete distribution with abundant usage. Hypergeometric distribution frequently replaces a binomial distribution when it is desirable to make allowance for the finiteness of the population size. For example, an application of the hypergeometric distribution arises in describing a probability model for the number of children attacked by an infectious disease, when a fixed number of them are exposed to it. Exact confidence interval estimation of hypergeometric parameter is reviewed. We consider the performance of exact confidence interval estimates of hypergeometric parameter in terms of actual coverage probability by small sample Monte Carlo simulation.

• Communications for Statistical Applications and Methods
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• v.10 no.1
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• pp.1-9
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• 2003

In this article, we consider a Bayesian estimation method for the geometric mean of $textsc{k}$ exponential parameters, Using the Tibshirani's orthogonal parameterization, we suggest an invariant prior distribution of the $textsc{k}$ parameters. It is seen that the prior, probability matching prior, is better than the uniform prior in the sense of correct frequentist coverage probability of the posterior quantile. Then a weighted Monte Carlo method is developed to approximate the posterior distribution of the mean. The method is easily implemented and provides posterior mean and HPD(Highest Posterior Density) interval for the geometric mean. A simulation study is given to illustrates the efficiency of the method.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.18 no.1
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• pp.31-37
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• 2006

The present study has been experimentally investigated the effect of geometric and operating parameters on the two-phase flow distribution of refrigerants in a horizontal T-junction. The operating parameters were the kind of refrigerants (R-22, R- l34a, and R-410A), saturated temperature, and the inlet mass flux and quality. The geometric parameters were the tube diameter and the tube diameter ratio. The measured data of refrigerants were compared with the values predicted using the models developed by several researchers for air/water or steani/water two-phase flow. Among the operating parameters, the inlet Quality was the most sensitive to the mass flow rate ratio. Between the geometric parameters, the tube diameter ratio was more sensitive than tube diameter.

• Communications of the Korean Mathematical Society
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• v.14 no.2
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• pp.405-423
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• 1999

We consider a statistical multiplexer model with finite buffer capacity and finite number of independent identical 3-state bursty voice sources. The burstiness of the sources is modeled by describing both two different active periods (at the rate of one packet perslot) and the passive periods during which no packets are generated. Assuming a mixture of two geometric distributions for active period and a geometric distribution for passive period and geometric distribution for passive period, we derive the recursive algorithm for the probability mass function of the buffer contents (in packets). We also obtain loss probability and the distribution of packet delay. Numerical results show that the system performance deteriorates considerably as the variance of the active period increases. Also, we see that the loss probability of 2-state Markov models is less than that of 3-state Markov models.

• Structural Engineering and Mechanics
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• v.87 no.1
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• pp.85-94
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• 2023

In the present work, thermal buckling and post-buckling behaviors of imperfect graphene platelet reinforced metal foams (GPRMFs) doubly curved shells are examined. Material properties of GPRMFs doubly curved shells are presumed to be the function of the thickness. Reddy' shell theory incorporating geometric nonlinearity is utilized to derive the governing equations. Various types of the graphene platelets (GPLs) distribution patterns and doubly curved shell types are taken into account. The nonlinear equations are discretized for the case of simply supported boundary conditions. The thermal post-buckling response are presented to analyze the effects of GPLs distribution patterns, initial geometric imperfection, GPLs weight fraction, porosity coefficient, porosity distribution forms, doubly curved shell types. The results show that these factors have significant effects on the thermal post-buckling problems.

• International Journal of Highway Engineering
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• v.6 no.3 s.21
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• pp.55-64
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• 2004

Maximum dry unit weight, ${\gamma}_{dmax}$, is the most important engineering properties for subgrade soil. Existing models to predict ${\gamma}_{dmax}$ containing many parameters, seem to be rather complex. This paper presents new simple models to predict ${\gamma}_{dmax}$. for sandy soils, A number of sieve analysis and compaction tests for 36 types of sands were conducted to develop the regression-based models. Parameters used to estimate ${\gamma}_{dmax}$ are both the geometric mean and geometric standard deviation of the soils, or the particle-size distribution curve parameters. Maximum dry unit weights predicted by the models are in good agreement with the laboratory measurements for the soil samples obtained at 16 locations within the Korea.