Journal of the Korean Data and Information Science Society

한국데이터정보과학회 (The Korean Data and Information Science Society)
권호 표지

실제포함확률을 이용한 초기하분포 모수의 근사신뢰구간 추정에 관한 모의실험 연구

A simulation study for the approximate confidence intervals of hypergeometric parameter by using actual coverage probability

  • Kim, Dae-Hak (Department of mathematic, Catholic University of Daegu)
  • 투고 : 2011.10.31
  • 심사 : 2011.11.22
  • 발행 : 2011.12.01
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⟨ 이전 논문 다음 논문 ⟩

초록

본 연구는 초기하분포의 모수, 즉 성공의 확률에 대한 신뢰구간추정에 대하여 설펴보았다. 초기하분포의 성공의 확률에 대한 신뢰구간은 일반적으로 잘 알려져 있지 않으나 그 응용성과 활용성의 측면에서 신뢰구간의 추정은 상당히 중요하다. 본 논문에서는 초기하분포의 성공의 확률에 대한 정확신뢰구간과 이항분포와 정규분포에 의한 근사신뢰구간을 소개하고 여러 가지 모집단의 크기와 표본 수에 대하여, 그리고 몇 가지 관찰값에 대한 정확신뢰구간과 근사신뢰구간을 계산하고 소 표본의 경우에 모의실험을 통하여 실제포함확률의 측면에서 살펴보았다.

In this paper, properties of exact confidence interval and some approximate confidence intervals of hyper-geometric parameter, that is the probability of success p in the population is discussed. Usually, binomial distribution is a well known discrete distribution with abundant usage. Hypergeometric distribution frequently replaces a binomial distribution when it is desirable to make allowance for the finiteness of the population size. For example, an application of the hypergeometric distribution arises in describing a probability model for the number of children attacked by an infectious disease, when a fixed number of them are exposed to it. Exact confidence interval estimation of hypergeometric parameter is reviewed. We consider the approximation of hypergeometirc distribution to the binomial and normal distribution respectively. Approximate confidence intervals based on these approximation are also adequately discussed. The performance of exact confidence interval estimates and approximate confidence intervals of hypergeometric parameter is compared in terms of actual coverage probability by small sample Monte Carlo simulation.

키워드

참고문헌

  1. Agresti, A. and Coull, B. A. (1998). Approximate is better than "Exact" for interval estimation of binomial proportions. The American Statistician, 52, 119-126.
  2. Blyth, C.R. (1986). Approximate binomial confidence limits. Journal of the American Statistical Association, 81, 843-855. https://doi.org/10.1080/01621459.1986.10478343
  3. Blyth, C. R. and Still, H. A. (1983). Binomial confidence intervals. Journal of the American Statistical Association, 78, 108-116. https://doi.org/10.1080/01621459.1983.10477938
  4. Chen, H. (1990). The accuracy of approximate intervals for a binomial parameter. Journal of the American Statistical Association, 85, 514-518. https://doi.org/10.1080/01621459.1990.10476229
  5. Clopper, C. J. and Pearson, E. S. (1934). The use of confidence or fiducial limits illustrated in the case of the binomial. Biometrika, 26, 404-413. https://doi.org/10.1093/biomet/26.4.404
  6. Hald, A. (1952). Statistical theory with engineering applications, John Wiley, New York.
  7. IMSL. (1994). International mathematical and statistical libraries (FORTRAN subroutines for evaluating special functions), Version 3, Visual Numerics, Houston, Texas.
  8. Katz, L. (1953). Confidence intervals for the number showing a certain characteristic in a population when sampling is without replacement. Journal of American Statistical Association, 48, 256-261. https://doi.org/10.1080/01621459.1953.10483471
  9. Kim, D. (2010a). On the actual coverage probability of binomial parameter. Journal of the Korean Data & Information Science Society, 21, 737-745.
  10. Kim, D. (2010b). On the actual coverage probability of hypergeometric parameter. Journal of the Korean Data & Information Science Society, 21, 1109-1115.
  11. Leemis, L. M. and Trivedi, K. S. (1996). A comparison of approximate interval estimators for the bernoulli parameter. The American Statistician, 50, 63-68.
  12. Liberman, G. J. and Owen, D. B. (1961). Tables of the hypergeometric probability distributions, Stanford University Press, Stanford.
  13. Sahai, H. and Khurshid, A. (1995). A note on confidence intervals for the hypergeometric parameter in analyzing biomedical data. Computational Biological Medicine, 25, 35-38. https://doi.org/10.1016/0010-4825(95)98883-F
  14. SAS. (1990). SAS language : Reference, Version 6, First Edition, SAS Institute, Cary, North Carolina.