• Title, Summary, Keyword: Pareto Curve

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Estimations of Lorenz Curve and Gini Index in a Pareto Distribution

  • Woo, Jung Soo;Yoon, Gi Ern
    • Communications for Statistical Applications and Methods
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    • v.8 no.1
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    • pp.249-256
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    • 2001
  • We shall derive the MLE and UMVUE of Lorenz Curve and Gini Index in a Pareto distribution with the pdf(1.1) and their variances. And compare mean square errors(MSE) of the MLE and UMVUE of the Lorenz Curve and Gini Index in a Pareto distribution with pdf(1.1).

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Test for the Pareto Distribution Based on the Transformed Sample Lorenz Curve

  • Kang, Suk-Bok;Cho, Young-Suk
    • Proceedings of the Korean Statistical Society Conference
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    • pp.133-137
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    • 2002
  • A powerful and easily computed goodness-of-fit test for Pareto distribution which does not depend on the unknown location and scale parameters is proposed based on the transformed sample Lorenz curve. We compare the power of the proposed test statistic with the other goodness-of-fit tests for Pareto distribution against various alternatives through Monte Carlo methods.

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Goodness-of-Fit Test for the Pareto Distribution Based on the Transformed Sample Lorenz curve

  • Kang, Suk-Bok;Cho, Young-Suk
    • Journal of the Korean Data and Information Science Society
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    • v.13 no.1
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    • pp.113-119
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    • 2002
  • A powerful and easily computed goodness-of-fit test for Pareto distribution which does not depend on the unknown location and scale parameters is proposed based on the transformed sample Lorenz curve. We compare the power of the proposed test statistic with the other goodness-of-fit tests for Pareto distribution against various alternatives through Monte Carlo methods.

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A study on the optimal design of rope way (索道線路의 最適設計에 대한 硏究)

  • 최선호;박용수
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.11 no.1
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    • pp.26-35
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    • 1987
  • As an attempt to make the multi-objection for the line design of the rope way, the resulted formulas from the catenary curve as exact ones were summarized, and it was found out that the Kuhn-Tucker's optimality conditions and regions of the objective functions can analytically be expressed with dimensionless parameters. The Pareto's optimum solution set was analytically obtained through the objective function-the minimum relation of $W^{*}$, and $W^{*}$ is a trade-off relation. From this, The dimension of a rope and the value of an initial tension that are the standard in design of the rope way were determined. It was concluded that $V^{*}$ should become minimum, and that the ratio of the dimension of rope to the value of and initial tension become larger than superposition factor corresponding to curve AB.to curve AB.

Estimation of the Lorenz Curve of the Pareto Distribution

  • Kang, Suk-Bok;Cho, Young-Suk
    • Communications for Statistical Applications and Methods
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    • v.6 no.1
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    • pp.285-292
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    • 1999
  • In this paper we propose the several estimators of the Lorenz curve in the Pareto distribution and obtain the bias and the mean squared error for each estimator. We compare the proposed estimators with the uniformly minimum variance unbiased estimator (UMVUE) and the maximum likelihood estimator (MLE) in terms of the mean squared error (MSE) through Monte Carlo methods and discuss the results.

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Aerodynamic Characteristics and Shape Optimization of Airfoils in WIG Craft Considered Ground Effect (지면효과를 고려한 WIG 선 익형의 공력특성 및 형상최적화)

  • Lee, Ju-Hee;Kim, Byeong-Sam;Park, Kyoung-Woo
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.30 no.11
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    • pp.1084-1092
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    • 2006
  • Shape optimization of airfoil in WIG craft has been performed by considering the ground effect. The WIG craft should satisfy various aerodynamic characteristics such as lift, lift to drag ratio, and static height stability. However, they show a strong trade-off phenomenon so that it is difficult to satisfy aerodynamic properties simultaneously. Optimization is carried out through the multi-objective genetic algorithm. A multi-objective optimization means that each objective is considered separately instead of weighting. Due to the trade-off, pareto sets and non-dominated solutions can be obtained instead of the unique solution. NACA0015 airfoil is considered as a baseline model, shapes of airfoil are parameterized and rebuilt with four-Bezier curves. There are eighteen design variables and three objective functions. The range of design variables and their resolutions are two primary keys for the successful optimization. By two preliminary optimizations, the variation can be reduced effectively. After thirty evolutions, the non-dominated pareto individuals of twenty seven are obtained. Pareto sets are all the set of possible and excellent solution across the design space. At any selections of the pareto set, these are no better solutions in all design space.

Aerodynamic Optimization of 3 Dimensional Wing-In-Ground Airfoils Using Multi-Objective Genetic Algorithm (지면효과를 받는 3 차원 WIG 선의 익형 형상 최적화)

  • Lee, Ju-Hee;You, Keun-Yeal;Park, Kyoung-Woo
    • Proceedings of the KSME Conference
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    • pp.3080-3085
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    • 2007
  • Shape optimization of the 3-dimensional WIG airfoil with 3.0-aspect ratio has been performed by using the multi-objective genetic algorithm. The WIG ship effectively floating above the surface by the ram effect and the virtual additional aspect ratio by a ground is one of next-generation and cost-effective transportations. Unlike the airplane flying out of the ground effect, a WIG ship has possibility to capsize because of unsatisfying the static stability. The WIG ship should satisfy aerodynamic properties as well as a static stability. They tend to strong contradict and it is difficult to satisfy aerodynamic properties and static stability simultaneously. It is inevitable that lift force has to scarify to obtain a static stability. Multi-objective optimization technique that the individual objectives are considered separately instead of weighting can overcome the conflict. Due to handling individual objectives, the optimum cannot be unique but a set of nondominated potential solutions: pareto optimum. There are three objectives; lift coefficient, lift-to-drag ratio and static stability. After a few evolutions, the non-dominated pareto individuals can be obtained. Pareto sets are all the set of possible and excellent solution across the design space. At any selections of the pareto set, these are no better solutions in all design space

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Global Shape Optimization of Airfoil Using Multi-objective Genetic Algorithm (다목적 유전알고리즘을 이용한 익형의 전역최적설계)

  • Lee, Ju-Hee;Lee, Sang-Hwan;Park, Kyoung-Woo
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.29 no.10
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    • pp.1163-1171
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    • 2005
  • The shape optimization of an airfoil has been performed for an incompressible viscous flow. In this study, Pareto frontier sets, which are global and non-dominated solutions, can be obtained without various weighting factors by using the multi-objective genetic algorithm An NACA0012 airfoil is considered as a baseline model, and the profile of the airfoil is parameterized and rebuilt with four Bezier curves. Two curves, front leading to maximum thickness, are composed of five control points and the rest, from maximum thickness to tailing edge, are composed of four control points. There are eighteen design variables and two objective functions such as the lift and drag coefficients. A generation is made up of forty-five individuals. After fifteenth evolutions, the Pareto individuals of twenty can be achieved. One Pareto, which is the best of the . reduction of the drag furce, improves its drag to $13\%$ and lift-drag ratio to $2\%$. Another Pareto, however, which is focused on increasing the lift force, can improve its lift force to $61\%$, while sustaining its drag force, compared to those of the baseline model.

Genetic Algorithm based Methodology for an Single-Hop Metro WDM Networks

  • Yang, Hyo-Sik;Kim, Sung-Il;Shin, Wee-Jae
    • Proceedings of the Korea Institute of Convergence Signal Processing
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    • pp.306-309
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    • 2005
  • We consider the multi-objective optimization of a multi-service arrayed-waveguide grating-based single-hop metro WDM network with the two conflicting objectives of maximizing throughput while minimizing delay. We develop and evaluate a genetic algorithm based methodology for finding the optimal throughput-delay tradeoff curve, the so-called Pareto-optimal frontier. Our methodology provides the network architecture and the Medium Access Control protocol parameters that achieve the Pareto-optima in a computationally efficient manner. The numerical results obtained with our methodology provide the Pareto-optimal network planning and operation solution for a wide range of traffic scenarios. The presented methodology is applicable to other networks with a similar throughput-delay tradeoff.

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Multi-Objective Optimization for Orthotrpic Steel Deck Bridges (강상판교의 다목적 최적설계)

  • Cho, Hyo Nam;Chung, Jee Seung;Min, Dae Hong
    • Journal of Korean Society of Steel Construction
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    • v.14 no.3
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    • pp.395-402
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    • 2002
  • This study proposed a muti-objective optimum design method for rational optimizing of orthotropic steel deck bridges. This multi-objective optimum design method was found to be effective in optimizing multi-objective problems, considering cost and deflection functions. It may ve difficult to optimize orthotropic steel deck bridges using a conventional optimization, since the bridges have several parts and show complex structural behaviors. Therefore, the Pareto curve can be obtained by performing the multi-objective optimization for real orthotropic steel deck bridges, using the multi-level technique with excellent efficiency. A reasonable and economical design can be attained using the Parato curve in the cost and deflection functions of the bridge. Thus, more reasonable design values can be determined based on a comparison with those using a conventional design procedure.