• 한국정보처리학회논문지
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• 제4권2호
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• pp.483-490
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• 1997

비중심 $X^2$분포의 누적분포 함수의 계산은 $X^2$검정에서 검정력 계산에 요구된다. 비중심 $X^2$분포의 확률계산은 일반적으로 많은 시간이 소요될 뿐 아니라 정확성이 문제가 되어 여러 접근 방법들이 계산속도와 정확성을 고려하여 제시되었다. 따라서 본 논문에서는 기존의 비중심 $X^2$분포의 확률 계산 접근방법에 의한 계산결과를 비교하고 자유도와 비중심모수에 따른 효율적인 접근방법을 탐색하였다.

• 품질경영학회지
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• 제14권2호
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• pp.47-54
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• 1986

A different kind of approximation has been developed in connection with calculation of the normal family distributions in digital computer. These approximations usually employ polynomial expressions. They give quite high accuracy, sometimes only within definite limits on the values of the variable. Outside these limits they may give quite poor approximations. In this paper we compare these approximations by criteria of C.P.U. time and accuracy using micro computer. Approximation formulas given by Zelen and Severo (1984) are proven to give the most accurate results within allowable C.P.U. time.

• 한국전산구조공학회논문집
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• 제20권3호
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• pp.303-309
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• 2007

무한영역에서 진행하는 탄성파를 유한영역에서 수치적으로 해석하기 위해 많은 흡수경계조건들이 제안되어져 왔다. Paraxial 경계조건은 흡수경계조건의 하나로서 스칼라 및 탄성파 방정식의 paraxial 근사화를 통해 얻어지며, 그 성능이 우수하고 수치해석시 계산적 부담을 주지 않는다. 그러나 경계조건이 복잡한 편미분 방정식으로 표현되어 있어 유한요소해석으로의 적용이 어렵다. 본 논문에서는 penalty function method를 이용하여 전체 에너지 범함수와 paraxial 경계조건을 함께 변분정식화 함으로써 유한요소해석을 수행하였다. 유한요소해석에 가장 적용이 용이하며, 많이 사용되어지는 Lysmer-Kuhlemeyer의 흡수경계조건과 성능을 비교함으로써 연구결과의 타당성을 입증하였다.

• 응용통계연구
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• 제11권2호
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• pp.287-302
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• 1998

표본평균(sample mean)의 밀도함수(density function)와 분포함수(distribution function)에 대한 안부점 근사(saddlepoin\ulcorner approximation)는 Daniels(1954, 1987), Lugannani와 Rice(1980)등에 의하여 유도되었으며, 이 근사식들의 정확도는 대표본(large sample)의 경우는 물론 소표본(small sample)의 경우에도 매우 뛰어난 것으로 알려져 있다. 최근 Easton과 Ronchetti(1986)는 일반적 통계량(general statistics)의 밀도함수에 대한 안부점 근사법을 제안하였고, 분포함수에 대한 근사로는 밀도함수에 대한 안부점 근사식을 직접 수치적으로 적분하는 방법을 제안하였다. 본 논문에서는 일반적 통계량의 분포함수에 대한 안부점 근사법을 제안하고, 이를 표본분산(sample variance)과 스튜던트화 평균(studentizd mean)의 분포함수에 대한 근사에 적용하였다.

• Journal of the Korean Data and Information Science Society
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• 제7권2호
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• pp.189-201
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• 1996

In this paper, we study the saddlepoint approximations for the ratio of independent random variables. In Section 2, we derive the saddlepoint approximation to the density. And in Section 3, we derive two approximation formulae for the tail probability, one by following Daniels'(1987) method and the other by following Lugannani and Rice's (1980). In Section 4, we represent some numerical examples which show that the errors are small even for small sample size.

• ETRI Journal
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• 제16권1호
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• pp.35-43
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• 1994

In this paper, the robustness of the artificial neural networks to noise is demonstrated with a multilayer perceptron, and the reason of robustness is due to the statistical orthogonality among hidden nodes and its hierarchical information extraction capability. Also, the misclassification probability of a well-trained multilayer perceptron is derived without any linear approximations when the inputs are contaminated with random noises. The misclassification probability for a noisy pattern is shown to be a function of the input pattern, noise variances, the weight matrices, and the nonlinear transformations. The result is verified with a handwritten digit recognition problem, which shows better result than that using linear approximations.

• Communications for Statistical Applications and Methods
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• 제1권1호
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• pp.81-86
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• 1994

A Chi-square approximation to the distribution of product of independent Beta variates denoted by U is developed. The distribution is commonly used as a test criterion for the general linear hypothesis about the multivariate linear models. The approximation is obtained by fitting a logarithmic function of U to a Chi-square variate in terms of the first three moments. It is compared with the well known approximations due to Box(1949), Rao(1948), and Mudholkar and Trivedi(1980). It is found that the Chi-square approximation compares favorably with the other three approximations.

• Communications for Statistical Applications and Methods
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• 제29권4호
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• pp.471-486
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• 2022

Autoregressive moving average (ARMA) models involve nonlinearity in the model coefficients because of unobserved lagged errors, which complicates the likelihood function and makes the posterior density analytically intractable. In order to overcome this problem of posterior analysis, some approximation methods have been proposed in literature. In this paper we first review the main analytic approximations proposed to approximate the posterior density of ARMA models to be analytically tractable, which include Newbold, Zellner-Reynolds, and Broemeling-Shaarawy approximations. We then use the Kullback-Leibler divergence to study the relation between these three analytic approximations and to measure the distance between their derived approximate posteriors for ARMA models. In addition, we evaluate the impact of the approximate posteriors distance in Bayesian estimates of mean and precision of the model coefficients by generating a large number of Monte Carlo simulations from the approximate posteriors. Simulation study results show that the approximate posteriors of Newbold and Zellner-Reynolds are very close to each other, and their estimates have higher precision compared to those of Broemeling-Shaarawy approximation. Same results are obtained from the application to real-world time series datasets.

• 응용통계연구
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• 제22권6호
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• pp.1345-1353
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• 2009

We introduce a simple methodology, so-called generalized gamma-polynomial approximation, based on moment-matching technique to approximate survival and hazard functions in the context of parametric survival analysis. We use the generalized gamma-polynomial approximation to approximate the density and distribution functions of convolutions and finite mixtures of random variables, from which the approximated survival and hazard functions are obtained. This technique provides very accurate approximation to the target functions, in addition to their being computationally efficient and easy to implement. In addition, the generalized gamma-polynomial approximations are very stable in middle range of the target distributions, whereas saddlepoint approximations are often unstable in a neighborhood of the mean.

• 설비공학논문집
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• 제6권4호
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• pp.344-353
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• 1994

This study numerically analyzed the dynamic characteristics of the frequency response on the pneumatic transmission line with load impedances. The pressure transfer function is represented by the distributed parameter line model. To validate the mathematical approximations of Bessel function ratios, the results of frequency response in a blocked line were compared with those obtained by the Infinite-product, Brown's and Square-root approximations. Special emphasis was given to the frequency response characteristics on the pneumatic transmission line with load impedances. Computations were carried out for the wide range of parameters in terms of load capacitance ratio and load resistance ratio. The present results indicated that the theoretical model is capable of accurately predicting the frequency response characteristics for any configuration of a fluid transmission line.