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Testing for Failure Rate Ordering between Survival Distributions

Park, Chul-Gyu  
  • 초록

    We develop in this paper the likelihood ratio test (LRT) for testing $H_1 : F_1 \preceq F_2$ against $H_2 - H_1$ where $H_2$ imposes no restriction on $F_1$ and $F_2$ and ' $\preceq$ ' means failure rate ordering. Both one and two-sample problems will be considered. In the one-sample case, one of the two distributions is known, while we assume in the other case both are unknown. We derive the asymptotic null distribution of the LRT statistic which will be of chi-bar-square type. The main issue here is to determine the least favorable distribution which is stochastically largest within the class of null distributions.


  • 주제어

    Failure rate ordering .   Likelihood ratio test .   Chi-bar-square distribution .   Level probability .   Least favorable distribution.  

  • 참고문헌 (11)

    1. Tests for the equality of failure rates , Cheng,K.F. , Biometrika / v.72,pp.211-215,
    2. Contribution to rank order statistics: The twosample case , Savage,I.R. , Annals of Mathematical Statistics / v.27,pp.590-615,
    3. Comparing and testing under order relations between percentile residual life functions , Aly,E.E. , The Canadian Journal of Statistics / v.16,pp.337-369,
    4. Ross,S.M. , Stochastic Process / v.,pp.,
    5. Testing for the proportionality of cause specific hazard rates against ordered alternatives in the competing risks model , Dykstra,R.L.;Kochar,S.;Robertson,Tim , Technical Report 184, Department of Statistics and Actuarial Science / v.,pp.,
    6. Statistical inference for uniform stochastic ordering in several populations , Dykstra,R.L.;Kochar,S.;Robertson,Tim , The Annals of Statistics / v.19,pp.870-888,
    7. Distribution-free comparison of two probability distributions with reference to their hazard rates , Kochar,S. , Biometrika / v.66,pp.437-441,
    8. A new distribution-free test for the equality of two failure rates , Kochar,S. , Biometrika / v.68,pp.423-426,
    9. Robertson,Tim;Wright,F.T.;Dykstra,R.L. , Order Restricted Statistical Inference / v.,pp.,
    10. Comparison of life distributions of the basis of their percentile residual life functions , Joe,H.;Proschan,F. , The Canadian Journal of Statistics / v.12,pp.91-97,
    11. On tailordering and comparison of failure rates , Bagai,I.;Kochar,S.C. , Communications in Statistics Theory and Method / v.15,pp.1377-1388,

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