• 한국통계학회:학술대회논문집
• /
• 한국통계학회 2002년도 춘계 학술발표회 논문집
• /
• pp.49-54
• /
• 2002

For arbitrary random variables {$X_{n},n{\geq}1$}, the order of growth of the series. $S_{n}\;=\;{\sum}_{j=1}^n\;X_{j}$ is studied in this paper. More specifically, when the series S_{n}$ diverges almost surely, the strong law of large numbers $S_{n}/g_{n}^{-1}$($A_{n}{\psi}(A_{n}))\;{\rightarrow}\;0$ a.s. is constructed by extending the results of Petrov (1973). On the other hand, if the series $S_{n}$ converges almost surely to a random variable S, then the tail series $T_{n}\;=\;S\;-\;S_{n-1}\;=\;{\sum}_{j=n}^{\infty}\;X_{j}$ is a well-defined sequence of random variables and converges to 0 almost surely. For the almost surely convergent series $S_{n}$, a tail series strong law of large numbers $T_{n}/g_{n}^{-1}(B_{n}{\psi}^{\ast}(B_{n}^{-1}))\;{\rightarrow}\;0$ a.s., which generalizes the result of Klesov (1984), is also established by investigating the duality between the limiting behavior of partial sums and that of tail series. In particular, an example is provided showing that the current work can prevail despite the fact that previous tail series strong law of large numbers does not work.

• International Journal of Automotive Technology
• /
• 제7권7호
• /
• pp.859-866
• /
• 2006

This study employed the perturbation method, the Edgeworth series, the reliability optimization, the reliability sensitivity technique and the robust design to present a practical and effective approach for the robust reliability design of vehicle components with arbitrary distribution parameters on the condition of known first four moments of original random variables. The theoretical formulae of the robust reliability design for vehicle components with arbitrary distribution parameters are obtained. The reliability sensitivity is added to the reliability optimization design model and the robust reliability design is described as a multi-objection optimization. On the condition of known first four moments of original random variables, the respective program can be used to obtain the robust reliability design parameters of vehicle components with arbitrary distribution parameters accurately and quickly.

• Advances in aircraft and spacecraft science
• /
• 제4권5호
• /
• pp.585-611
• /
• 2017

This article covenants with the post buckling witticism of carbon nanotube reinforced composite (CNTRC) beam supported with an elastic foundation in thermal atmospheres with arbitrary assumed random system properties. The arbitrary assumed random system properties are be modeled as uncorrelated Gaussian random input variables. Unvaryingly distributed (UD) and functionally graded (FG) distributions of the carbon nanotube are deliberated. The material belongings of CNTRC beam are presumed to be graded in the beam depth way and appraised through a micromechanical exemplary. The basic equations of a CNTRC beam are imitative constructed on a higher order shear deformation beam (HSDT) theory with von-Karman type nonlinearity. The beam is supported by two parameters Pasternak elastic foundation with Winkler cubic nonlinearity. The thermal dominance is involved in the material properties of CNTRC beam is foreseen to be temperature dependent (TD). The first and second order perturbation method (SOPT) and Monte Carlo sampling (MCS) by way of CO nonlinear finite element method (FEM) through direct iterative way are offered to observe the mean, coefficient of variation (COV) and probability distribution function (PDF) of critical post buckling load. Archetypal outcomes are presented for the volume fraction of CNTRC, slenderness ratios, boundary conditions, underpinning parameters, amplitude ratios, temperature reliant and sovereign random material properties with arbitrary system properties. The present defined tactic is corroborated with the results available in the literature and by employing MCS.

• Journal of applied mathematics & informatics
• /
• 제18권1_2호
• /
• pp.247-259
• /
• 2005

Necessary and sufficient conditions, under which there exists (at least) a sequence of vectors of real numbers for which the distribution function (d.f.) of any vector of extreme order statistics converges to a non-degenerate limit, are derived. The interesting thing is that these conditions solely depend on the univariate marginals. Moreover, the limit splits into the product of the limit univariate marginals if all the bivariate marginals of the trivariate d.f., from which the sample is drawn, is of negative quadrant dependent random variables (r.v.'s). Finally, all these results are stated for the multivariate extremes with arbitrary dimensions.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 1996년도 Proceedings of the Korea Automatic Control Conference, 11th (KACC); Pohang, Korea; 24-26 Oct. 1996
• /
• pp.95-98
• /
• 1996

Universal Learning Network(U.L.N.), which can model and control the large scale complicated systems naturally, consists of nonlinearly operated nodes and multi-branches that may have arbitrary time delays including zero or minus ones. Therefore, U.L.N. can be applied to many kinds of systems which are difficult to be expressed by ordinary first order difference equations with one sampling time delay. It has been already reported that learning algorithm of parameter variables in U.L.N. by forward and backward propagation is useful for modeling, managing and controlling of the large scale complicated systems such as industrial plants, economic, social and life phenomena. But, in the previous learning algorithm of U.L.N., time delays between the nodes were fixed, in other words, criterion function of U.L.N. was improved by adjusting only parameter variables. In this paper, a new learning algorithm is proposed, where not only parameter variables but also time delays between the nodes can be adjusted. Because time delays are integral numbers, adjustment of time delays can be carried out by a kind of random search procedure which executes intensified and diversified search in a single framework.

• Korean Journal of Hydrosciences
• /
• 제5권
• /
• pp.45-55
• /
• 1994

A new method to estimate the mean areal precipitation using kriging is developed. Urlike the conventional approach, points for double and quadruple numerical integrations in the kriging equation are selected randomly, given the boundary of area of interest. This feature eliminates the conventional approach's necessity of dividing the area into subareas and calculating the center of each subarea, which in turn makes the developed method more powerful in the case of complex boundaries. The algorithm to select random points within an arbitrary boundary, based on the theory of complex variables, is described. The results of Monte Carlo simulation showed that the error associated with estimation using randomly selected points is inversely proportional to the square root of the number of sampling points.

• 물과 미래
• /
• 제26권2호
• /
• pp.79-87
• /
• 1993

크리깅을 이용하여 평균면적우량을 추정함에 있어 새로운 방법을 개발하였다. 이 방법은 크리깅 방정식에 나타나는 2중 및 4중 수치적분에 필요한 점들을 대상지역의 경계만 주면 임의로 추출하여 사용한다는 것이 기존의 방법과는 상이하다. 이로 인해 대상지역을 소구역으로 나누고, 각각의 중심점을 계산해야 했던 기존 방식의 난점을 극복하였으며, 따라서 본 연구에서 개발된 방법은 복잡한 경계를 갖는 지역의 경우 더욱 유용하다. 경계가 주어지면 그 안에서 점들을 임의로 추출하는 과정을 복소함수론에 기초한 알고리듬을 통하여 설명하였다. Monte Carlo 시뮬레이션의 결과, 개발된 방법에 의한 평균면적유량의 추정에 따른 오차는 추출점 수의 제곱근에 반비례하였다.

• International Journal of Aeronautical and Space Sciences
• /
• 제18권4호
• /
• pp.729-739
• /
• 2017

The objective of this study was to optimize minimum-energy impulsive spacecraft intercept using genetic algorithms. A mathematical model was established on two-body system based on f and g solution and universal variable to address spacecraft intercept problem for non-coplanar elliptical orbits. This nonlinear problem includes many local optima due to discontinuity and strong nonlinearity. In addition, since it does not provide a closed-form solution, it must be solved using a numerical method. Therefore, the initial guess is that a very sensitive factor is needed to obtain globally optimal values. Genetic algorithms are effective for solving these kinds of optimization problems due to inherent properties of random search algorithms. The main goal of this paper was to find minimum energy solution for orbit transfer problem. The numerical solution using initial values evaluated by the genetic algorithm matched with results of Hohmann transfer. Such optimal solution for unrestricted arbitrary elliptic orbits using universal variables provides flexibility to solve orbit transfer problems.

• 한국국방경영분석학회지
• /
• 제28권2호
• /
• pp.56-69
• /
• 2002

A technique of finding both probability density and distribution function for interkilling times is considered and demonstrated. An important result is that any arbitrary interfiring time random variables fit to this study, The interfiring renewal density function given a certain interfiring probability density function can be applied to obtain the corresponding interkilling renewal density function which helps us to estimate the expected number of killing events in a time period. The numerical inversion of Laplace transformation makes these possible and the results appear to be excellent. In case of ammunition supply is limited, an alternative way of getting the probability density function of time to the killing is investigated. The convolution technique may give us a means of settling for this new problem.

• 한국항만경제학회지
• /
• 제20권2호
• /
• pp.151-167
• /
• 2004

Traditional traffic forecast has employed regression analysis or time-series analysis based on past trends of explanatory variables. However, not existing but planned port facilities do not have historical data for traffic estimation. Consequently, arbitrary traffic allocation has been subject to researcher's intuition. In this paper, container throughput at New Incheon Outer-South Port will be estimated using stated preference(SP) and sample enumeration methodology on the basis of survey data about the choice behaviors of port users in a theoretical situation. In the SP survey, shippers, freight forwarders and carriers were required to answer a choice between two alternative ports: Busan and Incheon. Although total 27 scenarios of questionnaires were constructed with 3 levels of 3 explanatory variables, each interviewee was asked to answer for just 9 scenarios chosen at random. A binary choice logit model was applied to the survey data. The elasticity of travel time is estimated to be very high, implying that building New Incheon Outer-South Port could be effective in relieving the congestion of the Kyungin corridor. The analysis result shows that increasing service level at Incheon Port would bring in the substantial diversion of container cargo in the Capital region to Incheon Port from Busan Port.