Test

, Volume 13, Issue 2, pp 403–416 | Cite as

One- and two-sample prediction based on doubly censored exponential data and prior information

Article

Abstract

On the basis of a doubly censored sample from an exponential lifetime distribution, the problem of predicting the lifetimes of the unfailed items (one-sample prediction), as well as a second independent future sample from the same distribution (two-sample prediction), is addressed in a Bayesian setting. A class of conjugate prior distributions, which includes Jeffreys' prior as a special case, is considered. Explicit expressions for predictive densities and survivals are derived. Assuming squared-error loss, Bayes predictive estimators are obtained in closed forms (in particular, the estimator of the number of failures in a specified future time interval, is given analytically). Bayes prediction limits and predictive estimators under absolute-error loss can readily be computed using iterative methods. As applications, the total duration time in a life test and the failure time of ak-out-of-n system may be predicted. As an illustration, a numerical example is also included.

Key Words

Bayes predictive estimators Bayes prediction limits failure time data order statistics Type II censoring 

AMS subject classification

62F15 62N05 

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References

  1. Barlow, R. E. andProschan, F. (1988). Life distribution models and incomplete data. In P. R. Krishnaiah and C. R. Rao, eds.Handbook of Statistics, vol. 7, pp. 225–249. Elsevier.Google Scholar
  2. Elfessi, A. (1997). Estimation of a linear function of the parameters of an exponential distribution from doubly censored data.Statistics and Probability Letters, 36:251–259.MATHCrossRefMathSciNetGoogle Scholar
  3. Fernández, A. J. (2000). Estimation and hypothesis testing for exponential lifetime models with double censoring and prior information.Journal of Economic and Social Research, 2(2):1–17.Google Scholar
  4. Fernández, A. J., Bravo, J. I., andDe Fuentes, I. (2002). Computing maximum likelihood estimates from Type II doubly censored exponential data.Statistical Methods & Applications, 11:187–200.MATHCrossRefGoogle Scholar
  5. Hartigan, J. A. (1964). Invariant prior distributions.Annals of Mathematical Statistics, 35:836–845.MathSciNetGoogle Scholar
  6. Hsieh, H. K. (1996). Prediction intervals for Weibull observations, based on early-failure data.IEEE Transactions on Reliability, 45:666–670.CrossRefGoogle Scholar
  7. Jeffreys, H. (1961).Theory of Probability, Clarendom Press, Oxford.MATHGoogle Scholar
  8. LaRiccia, V. N. (1986). Asymptotically chi-squared distributed tests of normality for Type II censored samples.Journal of the American Statistical Association, 81:1026–1031.MATHCrossRefMathSciNetGoogle Scholar
  9. Lawless, J. F. (1982).Statistical Models and Methods for Lifetime Data. John Wiley, New York.MATHGoogle Scholar
  10. Madi, M. T. (2002). On the invariant estimation of an exponential scale using doubly censored data.Statistics and Probability Letters, 56:889–901.CrossRefMathSciNetGoogle Scholar
  11. Ogunyemi, O. T., andNelson, P. I. (1997). Prediction of gamma failure times.IEEE Transactions on Reliability, 46:400–405.CrossRefGoogle Scholar
  12. Raqab, M. Z. (1995). On the maximum likelihood prediction of the exponential distribution based on doubly Type II censored samples.Pakistan Journal of Statistics, 11:1–10.MATHMathSciNetGoogle Scholar
  13. Schneider, H. (1984). Simple and highly efficient estimators for censored normal samples.Biometrika, 71:412–414.CrossRefGoogle Scholar
  14. Schneider, H. andWeissfeld, L. (1986). Inference based on Type II censored samples.Biometrics, 42:531–536.CrossRefGoogle Scholar

Copyright information

© Sociedad Española de Estadistica e Investigación Operativa 2004

Authors and Affiliations

  1. 1.Departamento de Estadística, I. O. y ComputaciónUniversidad de La LagunaLa LagunaSpain

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