The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Bayesian Estimation of k-Population Weibull Distribution Under Ordered Scale Parameters

순서를 갖는 척도모수들의 사전정보 하에 k-모집단 와이블분포의 베이지안 모수추정

  • 손영숙 (전남대학교 자연과학대학 수학통계학부 통계학전공) ;
  • 김성욱 (한양대학교 과학기술대학 응용수학전공)
  • Published : 2003.09.01
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Abstract

The problem of estimating the parameters of k-population Weibull distributions is discussed under the prior of ordered scale parameters. Parameters are estimated by the Gibbs sampling method. Since the conditional posterior distribution of the shape parameter in the Gibbs sampler is not log-concave, the shape parameter is generated by the adaptive rejection sampling. Finally, we applied this estimation methodology to the data discussed in Nelson (1970).

순서화된 척도모수들의 사전정보를 가지는 k-모집단 와이블분포의 모수추정을 위한 베이지안방법이 제시된다. 모수추정은 깁스샘플링에 의해서 이루어지며, 특히 깁스샘플러에서 형태모수의 조건부 사후분포는 로그-오목함수이므로 적응기각표집(Adaptive Rejection Sampling: ARS)방법에 의해 모수생성을 하였다. 논의된 모수추정법을 전기 절연유체 고장시간자료에 적용하여 척도모수의 순서화정보를 반영한 경우와 그렇지 않은 경우를 비교하였다.

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References

  1. 응용통계연구 v.9 no.1 순서화 모수에 대한 베이지안 추정 정광모;정윤식
  2. Non-Uniform Random Variate Generation Devroye,L.
  3. Journal of the American Statistical Association v.87 Bayesian analysis of constrained parameter and truncated data problems using Gibbs sampling Gelfand,A.E.;Smith,A.F.M.;Lee,T.M. https://doi.org/10.2307/2290286
  4. IEEE Transactions on Pattern Analysis and Machine Intelligence Stochastic relaxation, Gibbs distributions and the Bayesian resoration of images Geman,S.;Geman,D.
  5. Applied Statistics v.44 no.4 Adaptive Rejection Metropolis Sampling within Gibbs Sampling Gilke,W.R.;Best,N.G.;Tan,K.K.C. https://doi.org/10.2307/2986138
  6. Applied Statistics v.41 no.2 Adaptive Rejection Sampling for Gibbs Sampling Gilks,W.R.;Wild,P. https://doi.org/10.2307/2347565
  7. Environmental and Ecological Statistics v.9 Bayesian analysis under ordered functions of parameters Molitor,J.;Sun,D. https://doi.org/10.1023/A:1015122221315
  8. General Electric Co. Technical Report 71-C-011 Statistical methods for accelerated lifetest data-the inverse power law model Nelson,W.B.
  9. Biometrika v.83 Frequentist validity of posterior quantiles for a two-parameter exponential family Sun,D.;Ye,K. https://doi.org/10.1093/biomet/83.1.55
  10. MATHLAB/Statistics Toolbox(Version 5.2) The MATH WORKS Inc.