• Communications for Statistical Applications and Methods
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• 제9권2호
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• pp.555-563
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• 2002

This paper discusses cubic equations in general saddlepoint approximations. Exact roots are found for various cases by trigonometric identities, the root which is appropriate for the general saddlepoint approximations is selected and discussed, and the defective cases in which the general saddlepoint approximations cannot be used are found.

• Kyungpook Mathematical Journal
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• 제57권3호
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• pp.493-502
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• 2017

We propose an accurate approximation method via discrete Krawtchouk orthogonal polynomials to the distribution of a sum of independent but non-identically distributed binomial random variables. This approximation is a weighted binomial distribution with no need for continuity correction unlike commonly used density approximation methods such as saddlepoint, Gram-Charlier A type(GC), and Gaussian approximation methods. The accuracy obtained from the proposed approximation is compared with saddlepoint approximations applied by Eisinga et al. [4], which are the most accurate method among higher order asymptotic approximation methods. The numerical results show that the proposed approximation in general provide more accurate estimates over the entire range for the target probability mass function including the right-tail probabilities. In addition, the method is mathematically tractable and computationally easy to program.

• 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.

• 품질경영학회지
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• 제27권1호
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• pp.46-58
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• 1999

The exact distributions of the sample variance $(S^2_n)$ and the estimator ($\hat{C}_p$) of the process capability index are not easily obtained in general. In this paper, the approximations using saddlepoint techniques to the distributions of these statistics are suggested and compared with the other approximation methods. For comparisons, the exact values obtained by extensive Monte-Carlo (simulation) studies are also given. As a result, the suggested approximation methods are very accurate even in moderate or small sample sizes and are easy to use. Also, the suggested methods can be adapted to approximate the distributions of more complicated statistics, including $\hat{C}_pk$ ,$\hat{C}_pm$, etc.