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Inferences Concerning Exponential Distributions in the Presence of Randomly Right Censored Data with Missing Censored Values

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Abstract

Inferences concerning exponential distributions are considered from a sampling theory viewpoint when the data are randomly right censored and the censored values are missing. Both one-sample and m-sample (m ≥ 2) problems are considered. Likelihood functions are obtained for situations in which the censoring mechanism is informative which leads to natural and intuitively appealing estimators of the unknown proportions of censored observations. For testing hypotheses about the unknown parameters, three well-known test statistics, namely, likelihood ratio test, score test, and Wald-type test are considered.

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References

  • F. J. Anscombe, “Normal likelihood functions,” Ann. Inst. Statist. Math. (Tokyo) vol. 16 pp. 1–19, 1964.

    Google Scholar 

  • N. Balakrishnan and A.P. Basu, Editors (1995). The Exponential Distribution: Theory, Methods and Applications, New York: Gordon and Breach, 1995.

    Google Scholar 

  • D. J. Bartholomew, “The sampling distribution of an estimate arising in life testing,” Technometrics vol. 5 pp. 361–374, 1963.

    Google Scholar 

  • A. P. Basu and J. K. Ghosh, “Asymptotic properties of a solution to the likelihood equation with life-testing applications,” J. Amer. Statist. Assn. vol. 75, pp. 410–414, 1980.

    Google Scholar 

  • D. R. Cox and D. Oakes, Analysis of Survival Data, Chapman and Hall: New York, 1984.

    Google Scholar 

  • H. Cramer, Mathematical Methods of Statistics, Princeton University Press: Princeton, N.J., 1946.

    Google Scholar 

  • X. J. Hu, J. F. Lawless, and K. Suzuki, “Nonparametric estimation of a lifetime distribution when censoring times are missing,” Technometrics vol. 40 pp. 3–13, 1998.

    Google Scholar 

  • R. A. Johnson and D. W. Wichern, Applied Multivariate Analysis, 3rd ed., Simon & Schuster: New Jersey, 1992.

    Google Scholar 

  • J. D. Kalbfleisch and R. L. Prentice, The Statistical Analysis of Failure Time Data, John Wiley: New York, 1980.

    Google Scholar 

  • J. S. Kim and F. Prochan, “Piecewise exponential estimator of survivor function,” IEEE Trans. Reliab. vol. 40 pp. 134–139, 1991.

    Google Scholar 

  • L. Lininger, M. H. Gail, S. B. Green, and D. P. Byar, “Comparison of four tests for equality of survival curves in the presence of stratification and censoring,” Biometrika vol. 66 pp. 419–428, 1979.

    Google Scholar 

  • J. F. Lawless, Statistical Models And Methods For Lifetime Data, John Wiley: New York, 1982.

    Google Scholar 

  • M. J. Phillips and T. J. Sweeting, “Estimation for censored exponential data when the censoring times are subject to error,” J. R. Statist. Soc. vol. 58 pp. 775–783, 1996.

    Google Scholar 

Download references

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Authors and Affiliations

  1. Cancer Center Biostatistics, Duke University Medical Center, Durham, N.C, 27710, USA

    Bahadur Singh

  2. Lineberger Comprehensive Cancer Center, University of North Carolina, Chapel Hill, NC, 27599-7295, USA

    Bahadur Singh

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  1. Bahadur Singh
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Singh, B. Inferences Concerning Exponential Distributions in the Presence of Randomly Right Censored Data with Missing Censored Values. Lifetime Data Anal 8, 69–88 (2002). https://doi.org/10.1023/A:1013522916356

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