• Communications for Statistical Applications and Methods
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• v.21 no.2
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• pp.183-191
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• 2014

We define a multivariate Cauchy distribution using a probability density function; subsequently, a Ferguson's definition of a multivariate Cauchy distribution can be viewed as a characterization theorem using the characteristic function approach. To clarify this characterization theorem, we construct two dependent Cauchy random variables, but their sum is not Cauchy distributed. In doing so the proofs depend on the characteristic function, but we use the cumulative distribution function to obtain the exact density of their sum. The derivation methods are relatively straightforward and appropriate for graduate level statistics theory courses.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.11
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• pp.1051-1058
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• 2011

The military communication equipment is required the high reliability for operating adequate functions under severe conditions. This reliability is the essential element for the quality of the product, for the uncontrolled factors, such as the clearance, damage of the material, the reduction of stiffness, which are the designer is unable to handle. In this paper, the uncertainty for the dimension was supposed to the probability model for the military communication equipment, and the average of the objective function was minimized for reducing design uncertainty. The reliability-based design optimization which was implemented the limit state function was formulated into the mathematical model, so the reliable optimized structure was implemented than the base-line design.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2011.10a
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• pp.504-509
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• 2011

The military communication equipment is required the high reliability for operating adequate functions under severe conditions. This reliability is the essential element for the quality of the product, for the uncontrolled factors, such as the clearance, damage of the material, the reduction of stiffness, which are the designer is unable to handle. In this paper, the uncertainty for the design was supposed to the probability model for the military communication equipment, and the average of the objective function was minimized for reducing design uncertainty. The reliability-based design optimization which was implemented the limit state function was formulated into the mathematical model, so the reliable optimized structure was implemented than the base-line design.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2005.06a
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• pp.690-693
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• 2005

In this paper, probabilistic distribution of fatigue life of chassis component is determined statistically by applying the design of experiments and the Pearson system. To construct $p-\varepsilon-N$ curve, the case that fatigue data are random variables is attempted. Probabilistic density function(p.d.f) for fatigue life is obtained by design of experiment and using this p.d.f fatigue reliability about any aimed fatigue life can be calculated. Lower control arm and rear torsion bar of chassis component are selected as examples for analysis. Component load histories, which are obtained by multi-body dynamic simulation for Belsian load history, are used. Finite element analysis are performed using commercial software MSC Nastran and fatigue analysis are performed using FE Fatigue. When strain-life curve itself is random variable, probability density function of fatigue life has very little difference from log-normal distribution. And the case of fatigue data are random variables, probability density functions are approximated to Beta distribution. Each p.d.f is verified by Monte-Carlo simulation.

• Journal of the Korean Society for Precision Engineering
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• v.24 no.2 s.191
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• pp.110-117
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• 2007

In this paper, probabilistic distribution of chassis component fatigue life is determined statistically by applying the design of experiments and the Pearson system. To construct p - ${\varepsilon}$ - N curve, the case that fatigue data are random variables is attempted. Probabilistic density function (p.d.f) for fatigue life is obtained by the design of experiment and using this p.d.f fatigue reliability, any aimed fatigue life can be calculated. Lower control arm and rear torsion bar of chassis components are selected as examples for analysis. Component load histories which are obtained by multi-body dynamic simulation for Belsian load history are used. Finite element analysis is performed by using commercial software MSC Nastran and fatigue analysis is performed by using FE Fatigue. When strain-life curve itself is random variable, the probability density function of fatigue life has very little difference from log-normal distribution. And the cases of fatigue data are random variables, probability density functions are approximated to Beta distribution. Each p.d.f is verified by Monte-Carlo simulation.

• Journal of the Korean Data and Information Science Society
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• v.16 no.3
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• pp.705-712
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• 2005

Entropy is the basic concept of information theory. It is well defined for random varibles with known probability density function(pdf). For given data with unknown pdf, entropy should be estimated. Usually, estimation of entropy is based on the approximations. In this paper, we consider a kernel based approximation and compare it to the cumulant approximation method for several distributions. Monte carlo simulation for various sample size is conducted.

• Journal of ILASS-Korea
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• v.5 no.1
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• pp.30-40
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• 2000

The characteristics of liquefied butane spray are expected to be different from conventional diesel fuel spray, because a kind of flash boiling spray is expected when the back pressure is below the saturated vapor pressure of the butane(0.23MPa at 298K). The ambient pressure was held at a pressure above(0.37MPa) and below(0.15MPa) the fuel vapor pressure. The axial velocities, radial velocities, and size distributions in butane sprays were measured with PDPA(Phase Doppler Particle Analyzer) system. The PDPA measurement showed a smaller SMD at the 0.15MPa chamber pressure, compared to the 0.37MPa case. Log-hyperbolic density function for the droplets size distribution can be fitted to the experimental results of a liquefied butane spray.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.47-55
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• 2003

This paper Presents active control algorithm using probability density function of structural energy. It is assumed that the structural energy under excitation has Rayleigh probability distribution. This assumption is based on the fact that Rayleigh distribution satisfies the condition that the structural energy is always positive and the occurrence probability of minimum energy is zero. The magnitude of control force is determined by the probability that the structural energy exceeds the specified target critical energy, and the sign of control force is determined by Lyapunov controller design method. Proposed control algorithm shows much reduction of peak responses under seismic excitation compared to LQR controller, and it can consider control force limit in the controller design. Also, chattering problem which sometimes occurs in Lyapunov controller can be avoided.

• Proceedings of the IEEK Conference
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• 2008.06a
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• pp.155-156
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• 2008

This paper provides a general and compact expression for the probability density function (pdf) and the moment-generating function (MGF) of the maximal ratio combiner output over Rayleigh fading channels. It is then used to derive closed form expression outage probability for repetition code problem. A variety of simulations is performed and shows that they match exactly with analytic ones.

• Current Optics and Photonics
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• v.3 no.4
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• pp.311-319
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• 2019

A hybrid free-space-optical/radio-frequency (FSO/RF) communication system is considered, with the help of amplify-and-forward (AF) relaying. We consider various weather conditions to investigate their effects on the system's performance. We begin by obtaining the cumulative distribution function and probability density function of the end-to-end signal-to-noise ratio for the AF dual-hop FSO communication system with RF backup link. Then, these results are used to derive closed-form expressions for the outage probability, average bit-error rate, and average ergodic capacity. The results show that the considered system efficiently employs the complementary nature of FSO and RF links, resulting in impressive performance improvements compared to non-hybrid systems.