• Computers and Concrete
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• v.21 no.2
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• pp.181-187
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• 2018

In order to solve the life prediction problem of damaged coating steel bar in magnesium cement concrete, this study tries to establish the marginal distribution function by using the corrosion current density as a single degradation factor. Representing the degree of steel corrosion, the corrosion current density were tested in electrochemical workstation. Then based on the Copula function, the joint distribution function of the damaged coating was established. Therefore, it is indicated that the corrosion current density of the bare steel and coated steel bar can be used as the boundary element to establish the marginal distribution function. By using the Frank-Copula function of Copula Archimedean function family, the joint distribution function of the damaged coating steel bar was successfully established. Finally, the life of the damaged coating steel bar has been lost in 7320d. As a new method for the corrosion of steel bar under the multi-dimensional factors, the two-dimensional Copula function has certain practical significance by putting forward some new ideas.

• Journal of the Korean Data and Information Science Society
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• v.20 no.1
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• pp.191-202
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• 2009

In this study, we drive the one dimensional marginal transform function, probability density function and probability distribution function for the random variables $T_{{\xi}N}$ (Time taken by the servers during the vacations), ${\xi}_N$(Number of vacations taken by the servers) and ${\eta}_N$(Number of customers or units arrive in the system) by controlling the variability of two random variables simultaneously.

• International Journal of Reliability and Applications
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• v.10 no.2
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• pp.63-79
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• 2009

A new bivariate linear failure rate distribution is introduced through a shock model. It is proved that the marginal distributions of this new bivariate distribution are linear failure rate distributions. The joint moment generating function of the bivariate distribution is derived. Mixtures of bivariate linear failure rate distributions are also discussed. Application to a real data is given.

• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.363-374
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• 2006

A new bivariate beta distribution based on the Appell function of the third kind is introduced. Various representations are derived for its product moments, marginal densities, marginal moments, conditional densities and conditional moments. The method of maximum likelihood is used to derive the associated estimation procedure as well as the Fisher information matrix.

• Communications for Statistical Applications and Methods
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• v.31 no.1
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• pp.65-85
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• 2024

The tail probability of a function of a multivariate random variable is not easy to estimate by the crude Monte Carlo simulation. When the occurrence of the function value over a threshold is rare, the accurate estimation of the corresponding probability requires a huge number of samples. When the explicit form of the cumulative distribution function of each component of the variable is known, the inverse transform likelihood ratio method is directly applicable scheme to estimate the tail probability efficiently. The method is a type of the importance sampling and its efficiency depends on the selection of the importance sampling distribution. When the cumulative distribution of the multivariate random variable is represented by a copula and its marginal distributions, we develop an iterative algorithm to find the optimal importance sampling distribution, and show the convergence of the algorithm. The performance of the proposed scheme is compared with the crude Monte Carlo simulation numerically.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.1
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• pp.1-3
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• 2009

Recently, Carlsson, Full\acute{e}$r and Majlender [1] presented the concept of possibilitic correlation representing an average degree of interaction between marginal distribution of a joint possibility distribution as compared to their respective dispersions. They also formulated the weak and strong forms of the possibilistic Cauchy-Schwarz inequality. In this paper, we define a new probability measure. Then the weak and strong forms of the Cauchy-Schwarz inequality are immediate consequence of probabilistic Cauchy-Schwarz inequality with respect to the new probability measure.

• 한국지구물리탐사학회:학술대회논문집
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• 2003.11a
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• pp.340-343
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• 2003

This study presents a practical procedure for the Bayesian inversion of geophysical data by Markov chain Monte Carlo (MCMC) sampling and geostatistics. We have applied geostatistical techniques for the acquisition of prior model information, and then the MCMC method was adopted to infer the characteristics of the marginal distributions of model parameters. For the Bayesian inversion of dipole-dipole array resistivity data, we have used the indicator kriging and simulation techniques to generate cumulative density functions from Schlumberger array resistivity data and well logging data, and obtained prior information by cokriging and simulations from covariogram models. The indicator approach makes it possible to incorporate non-parametric information into the probabilistic density function. We have also adopted the MCMC approach, based on Gibbs sampling, to examine the characteristics of a posteriori probability density function and the marginal distribution of each parameter. This approach provides an effective way to treat Bayesian inversion of geophysical data and reduce the non-uniqueness by incorporating various prior information.

• Wind and Structures
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• v.31 no.6
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• pp.549-560
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• 2020

Methods for stochastic simulation of non-Gaussian wind pressure have increasingly addressed the efficiency and accuracy contents to offer an accurate description of the extreme value estimation of the long-span and high-rise structures. This paper presents a linear prediction and z-transform (LPZ) based Cumulative distribution function (CDF) mapping algorithm for the simulation of multivariate non-Gaussian fluctuating wind pressure. The new algorithm generates realizations of non-Gaussian with prescribed marginal probability distribution function (PDF) and prescribed spectral density function (PSD). The inverse linear prediction and z-transform function (ILPZ) is deduced. LPZ is improved and applied to non-Gaussian wind pressure simulation for the first time. The new algorithm is demonstrated to be efficient, flexible, and more accurate in comparison with the FFT-based method and Hermite polynomial model method in two examples for transverse softening and longitudinal hardening non-Gaussian wind pressures.

• Journal of Labour Economics
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• v.29 no.2
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• pp.67-116
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• 2006

This study directly analyzes the wage distributions rather than indirectly looking at a few of their moments. It also investigates wage distributions using various descriptive and semi-parametric methods. The wage distributions of Korean manufacturing industries can in general be represented by three distinct forms, underdeveloped, advanced and the medium of the two. The discrepancies in these distribution forms are explained by differences in the labor-type distributions and their weights in the composition of wage distribution forms, and further clarified through various descriptive statistics based on them. However, the descriptive statistical analysis has a limit in that it shows mixed outcomes of different categoric variables. Then, this problem is resolved by applying a semi-parametric estimation of hazard function and the marginal effect evaluations of variable changes on estimated distributions not on the function. As a result of this marginal analysis, the common features and differences of categoric variables and their intensities of effects on distributions are revealed.

• Journal of Periodontal and Implant Science
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• v.36 no.2
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• pp.531-554
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• 2006

Oral implants must fulfill certain criteria arising from special demands of function, which include biocompatibility, adequate mechanical strength, optimum soft and hard tissue integration, and transmission of functional forces to bone within physiological limits. And one of the critical elements influencing the long-term uncompromise functioning of oral implants is load distribution at the implant- bone interface, Factors that affect the load transfer at the bone-implant interface include the type of loading, material properties of the implant and prosthesis, implant geometry, surface structure, quality and quantity of the surrounding bone, and nature of the bone-implant interface. To understand the biomechanical behavior of dental implants, validation of stress and strain measurements is required. The finite element analysis (FEA) has been applied to the dental implant field to predict stress distribution patterns in the implant-bone interface by comparison of various implant designs. This method offers the advantage of solving complex structural problems by dividing them into smaller and simpler interrelated sections by using mathematical techniques. The purpose of this study was to evaluate the stresses induced around the implants in bone using FEA, A 3D FEA computer software (SOLIDWORKS 2004, DASSO SYSTEM, France) was used for the analysis of clinical simulations. Two types (external and internal) of implants of 4.1 mm diameter, 12.0 mm length were buried in 4 types of bone modeled. Vertical and oblique forces of lOON were applied on the center of the abutment, and the values of von Mises equivalent stress at the implant-bone interface were computed. The results showed that von Mises stresses at the marginal. bone were higher under oblique load than under vertical load, and the stresses were higher at the lingual marginal bone than at the buccal marginal bone under oblique load. Under vertical and oblique load, the stress in type I, II, III bone was found to be the highest at the marginal bone and the lowest at the bone around apical portions of implant. Higher stresses occurred at the top of the crestal region and lower stresses occurred near the tip of the implant with greater thickness of the cortical shell while high stresses surrounded the fixture apex for type N. The stresses in the crestal region were higher in Model 2 than in Model 1, the stresses near the tip of the implant were higher in Model 1 than Model 2, and Model 2 showed more effective stress distribution than Model.