Communications for Statistical Applications and Methods

  • 제2권2호
  • /
  • Pages.336-346
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  • 1995
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  • 2287-7843(pISSN)
  • /
  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지

Applications of Saddlepoint Method to Stress-Strength Model

  • Na, Jong-Hwa (Stasistical Research Institute, College of Natural Science, Seoul National University) ;
  • Kim, Woo-Chul (Department of Computer Science and Statistics, Seoul National University)
  • 발행 : 1995.12.01
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초록

In many problems concerned with statistical inferences, it will be of interest to compute tail areas rather than densities. But, it is often hard to calculate the exact tail probability. Saddlepoint approximation formula to the tail probability of a smooth function of random cector is developed by DiCiccio and Martin(1991). Applications of this method to stress-strength model are considered in this paper. To obtain the generalized p-values suggested by Tsui and Weerahandi(1989), we need to calculate complicated multiple integration. However, DiCiccio and Martin's(1991) results offer a convenient method to approximate these very accurately. For many artificial data sets, we access the accuracy of DiCiccio and Martin's by comparing the approximate value with the exact one.

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참고문헌

  1. Scandinavian Journal of Statistics v.17 A note on the standardized signed log-likelihood ratio Barndorff-Nielsen,O.E.
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  3. Annals of Mathematical Statistics v.25 Saddlepoint approximations in statistics Daniels,H.E.
  4. International Statistical Review v.55 no.1 Tail probability approximations Daniels,H.E.
  5. Biometrika v.78 Approximations of marginal tail probabilities for a class of smooth functions with applications to Bayesian and conditional inference DiCiccio,T.J.;Martin,M.A.
  6. Biometrika v.77 Tail probabilities from observed likelihood Fraser,D.A.S.
  7. Advences in Applied Probability v.12 Saddle point approximation for the distribution of the sum of independent random variables Lugannani,R.;Rice,S.
  8. Journal of American Statistical Association v.84 no.406 Generalized p-values in significance testing of hypotheses in the presence of nuisance parameter Tsui,K.W.;Weerahandi,S.
  9. Advences in Applied Probability v.27 Saddlepoint approximations for bivariate distribution Wang,S.
  10. Technometrics v.34 no.1 Testing reliability in a stress-strength model when x and y are normally distributed Weerahandi,S.;Johnson,R.A.