Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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Saddlepoint approximation for distribution function of sample mean of skew-normal distribution

왜정규 표본평균의 분포함수에 대한 안장점근사

  • Na, Jong-Hwa (Department of Information and Statistics, Chungbuk National University) ;
  • Yu, Hye-Kyung (Korea National Institute of Health)
  • Received : 2013.08.05
  • Accepted : 2013.08.30
  • Published : 2013.11.30
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Abstract

Recently, the usage of skew-normal distribution, instead of classical normal distribution, is rising up in many statistical theories and applications. In this paper, we deal with saddlepoint approximation for the distribution function of sample mean of skew-normal distribution. Comparing to normal approximation, saddlepoint approximation provides very accurate results in small sample sizes as well as for large or moderate sample sizes. Saddlepoint approximations related to the skew-normal distribution, suggested in this paper, can be used as a approximate approach to the classical method of Gupta and Chen (2001) and Chen et al. (2004) which need very complicate calculations. Through simulation study, we verified the accuracy of the suggested approximation and applied the approximation to Robert's (1966) twin data.

최근 많은 통계 이론과 응용 문제에 정규분포의 대안으로 왜정규분포에 대한 활용이 높아지고 있다. 본 논문에서는 왜정규분포에 기반한 표본평균의 분포함수에 대한 안장점근사를 다루었다. 안장점근사는 기존의 정규근사에 비해 매우 뛰어난 정확성을 보일 뿐 아니라, 소표본에서도 정확한 근사결과를 제공한다. 본 논문에서 제시한 왜정규분포에 관련된 안장점근사는 복잡한 계산이 요구되는 기존의 Gupta와 Chen (2001)과 Chen 등 (2004)에 대한 근사적 방법으로 사용될 수 있다. 모의실험을 통해 표본평균의 분포함수에 대한 제안된 안장점근사의 정확도를 확인하고, 실제 자료에 대한 응용으로 Roberts (1966)의 쌍둥이 자료의 분석에 적용하였다.

Keywords

References

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