×

zbMATH — the first resource for mathematics

On estimation of \(R=P(Y<X)\) for exponential distribution under progressive type-II censoring. (English) Zbl 1431.62463
Summary: This paper deals with the estimation of the stress-strength parameter \(R=P(Y<X)\), when \(X\) and \(Y\) are independent exponential random variables, and the data obtained from both distributions are progressively type-II censored. The uniformly minimum variance unbiased estimator and the maximum-likelihood estimator (MLE) are obtained for the stress-strength parameter. Based on the exact distribution of the MLE of \(R\), an exact confidence interval of \(R\) has been obtained. Bayes estimate of \(R\) and the associated credible interval are also obtained under the assumption of independent inverse gamma priors. An extensive computer simulation is used to compare the performances of the proposed estimators. One data analysis has been performed for illustrative purpose.

MSC:
62N05 Reliability and life testing
62N02 Estimation in survival analysis and censored data
62F10 Point estimation
62F15 Bayesian inference
62F25 Parametric tolerance and confidence regions
PDF BibTeX Cite
Full Text: DOI
References:
[1] Birnbaum, Z. W. On a use of Mann–Whitney statistics. Proceedings of the Third Berkley Symposium in Mathematics, Statistics and Probability. Vol. 1, pp.13–17. Berkley, CA: University of California Press.
[2] DOI: 10.1142/9789812564511
[3] DOI: 10.1007/s001840400345 · Zbl 1079.62032
[4] DOI: 10.1109/TR.2006.874918
[5] DOI: 10.1081/SAC-200055741 · Zbl 1065.62172
[6] DOI: 10.1016/j.spl.2009.05.026 · Zbl 1169.62012
[7] DOI: 10.1080/03610920802162664 · Zbl 1292.62041
[8] Saraçoğlu B., Selçuk J. Appl. Math. 8 pp 25– (2007)
[9] Saraçoğlu B., Hacet. J. Math. Stat. 38 pp 339– (2009)
[10] DOI: 10.1007/s00184-006-0074-7 · Zbl 1433.62061
[11] DOI: 10.1007/s00362-006-0310-2 · Zbl 1125.62021
[12] DOI: 10.1007/s00362-006-0034-3 · Zbl 1312.62129
[13] DOI: 10.1023/A:1011352923990 · Zbl 0984.62082
[14] Balakrishnan N., Progressive Censoring: Theory, Methods and Applications (2000)
[15] DOI: 10.1007/s11749-007-0061-y · Zbl 1121.62052
[16] DOI: 10.2307/1267617 · Zbl 0292.62021
[17] Bailey W. N., Generalized Hypergeometric Series (1935) · Zbl 0011.02303
[18] Ferguson T., Mathematical Statistics: A Decision Theoretic Approach (1967)
[19] DOI: 10.1007/BF02242271 · Zbl 0561.65004
[20] DOI: 10.1016/j.compositesa.2008.10.001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.