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.
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Fernández, A.J. One- and two-sample prediction based on doubly censored exponential data and prior information. Test 13, 403–416 (2004). https://doi.org/10.1007/BF02595779
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DOI: https://doi.org/10.1007/BF02595779
Key Words
- Bayes predictive estimators
- Bayes prediction limits
- failure time data
- order statistics
- Type II censoring