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Inference procedures in some bivariate exponential models under hybrid random censoring

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Abstract

We consider a life testing experiment in whichn units are put on test, successive lifetimes (X 1,X 2) of both componentsC 1 andC 2 are recorded and the observation is terminated either at ther-th order statistic ofY i =Min(X 1i ,X 2i ),i=1,…,n i.e.Y (r) or a random timeT i whichever is reached first. This mixture of random censoring and type-II censoring schemes, we call as hybrid random censoring which is of wide use. We use this censoring scheme and obtain maximum likelihood estimation of the parameters and develop large sample tests in bivariate exponential (BVE) models proposed by Marshall-Olkin (1967), Block-Basu (1974), Freund (1961) and Preschan-Sullo (1974).

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References

  • Block, H. W. and Basu, A. P. (1974). A continuous bivariate exponential extension.Journal of the American Statistical Association, 69, 1031–37.

    Article  MATH  MathSciNet  Google Scholar 

  • Chen Shu-Mei and Bhattacharrya, G.K. (1988). Exact confidence bounds for an exponential parameter under hybrid censoring.Comm. Statistics, Theory-Methods, 17(6), 1857–70.

    Article  MATH  Google Scholar 

  • Ebrahimi, N. (1990). Estimating the parameter of an exponential distribution from hybrid life test.Journal of Statistical Planning and Inference, 23, 255–61.

    MathSciNet  Google Scholar 

  • Ebrahimi, N. (1992). Prediction intervalls for future failures in the exponential distribution under hybrid censoring,IEEE Tran. on Relliability, 41, 127–32.

    Article  MATH  Google Scholar 

  • Epstein, B. (1954). Truncated life tests in the exponential case.Annals of Mathematical Statistics, 25, 555–64.

    Article  MathSciNet  Google Scholar 

  • Fairbanks, K., Madson, R. and Dykstra (1962). A confidence interval for an exponential parameter from a hybvrid life test.Journal of the American Statistical Association, 77, 137–40.

    Article  Google Scholar 

  • Freund, J.E. (1961). A bivariate extension of the exponential distribution.Journal of the American Statistical Association, 56, 971–77.

    Article  MATH  MathSciNet  Google Scholar 

  • Hanagal, D.D. (1992a). Some inference results in bivariate exponential distributions based on censored samples.Comm. Statistics, Theory Methods, 21(5), 1273–95.

    Article  MATH  MathSciNet  Google Scholar 

  • Hanagal, D.D. (1992b). Some inference results in modified Freund's bivariate exponential distribution.Biometrical Journal, 34(6), 745–56.

    Article  MATH  Google Scholar 

  • Hanagal, D.D. (1992c). Inference results in some bivariate exponential models based on censoring. Proceedings of the symposium on Statistical Inference held at Trivendrum, India during June 17–19, 1992. Centre for Mathematical Sciences, India, 23, 83–92.

    Google Scholar 

  • Hanagal, D. D. and Kale, B. K. (1991a). Large sample tests of independence for an absolutely continuous bivariate exponential distribution.Comm. Statistics, Theory-Methods, 20, 1301–13.

    Article  MathSciNet  Google Scholar 

  • Hanagal, D. D. and Kale, B. K. (1991b). Large sample tests of λ3 in the bivariate exponential distribution.Statistics and Probability Letters, 12, 311–13.

    Article  MathSciNet  Google Scholar 

  • Hanagal, D. D. and Kale, B. K. (1992). Large sample tests for testing symmetry, and independence in some bivariate exponential models.Comm. Statistics, Theory-Methods, 21, 2625–43.

    Article  MATH  MathSciNet  Google Scholar 

  • Leurgans, S., Tsai Wei-Yan and Crowley, T. (1972). Freund's bivariate exponential distribution and censoring.I.M.S. Lecture Notes, Monographn Ser. Vol. 2, 230–242.

    Google Scholar 

  • Marshall, A.W. and Olkin, I. (1967). A multivariate exponential distribution.Journal of the American Statistical Association, 62, 30–44.

    Article  MATH  MathSciNet  Google Scholar 

  • MIL-STD-781C (1977). Reliability Design Qualifications and Production Acceptance Tests, Exponential Distribution, Washington, D.C., U.S. Government Printing Office.

    Google Scholar 

  • Proschan, F. and Sullo, P. (1974). Estimating the parameters of bivariate exponential distributions in several sampling situations. Reliability and biometry eds. F. Proschan and R.J. Serfling, Philadelphia: SIAM, 423–40.

    Google Scholar 

  • Rao, C. R. (1973). Linear Statistical Inference and Its Applications: 2nd Edition. Wiley Eastern Ltd.

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  1. Department of Statistics, University of Pune, 411007, Pune, India

    David D. Hanagal

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  1. David D. Hanagal
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Hanagal, D.D. Inference procedures in some bivariate exponential models under hybrid random censoring. Statistical Papers 38, 167–189 (1997). https://doi.org/10.1007/BF02925222

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  • DOI: https://doi.org/10.1007/BF02925222

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