Exact likelihood inference for the exponential distribution under generalized type-I and type-II hybrid censoring.

*(English)*Zbl 1162.62317Summary: S.-M. Chen and G. K. Bhattacharyya [Commun. Stat., Theory Methods 17, No. 6, 1857–1870 (1988; Zbl 0644.62101)] considered a hybrid censoring scheme and obtained the exact distribution of the maximum likelihood estimator of the mean of an exponential distribution along with an exact lower confidence bound. A. Childs et al. [Ann. Inst. Stat. Math. 55, No. 2, 319–330 (2003; Zbl 1049.62021)] recently derived an alternative simpler expression for the distribution of the MLE. These authors also proposed a new hybrid censoring scheme and derived similar results for the exponential model. We propose two generalized hybrid censoring schemes which have some advantages over the hybrid censoring schemes already discussed in the literature. We then derive the exact distribution of the maximum likelihood estimator as well as exact confidence intervals for the mean of the exponential distribution under these generalized hybrid censoring schemes.

##### MSC:

62F10 | Point estimation |

62N01 | Censored data models |

62E15 | Exact distribution theory in statistics |

62F25 | Parametric tolerance and confidence regions |

62N05 | Reliability and life testing |

##### Keywords:

maximum likelihood estimator; likelihood inference; hybrid censoring; exponential distribution; life testing
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\textit{B. Chandrasekar} et al., Nav. Res. Logist. 51, No. 7, 994--1004 (2004; Zbl 1162.62317)

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##### References:

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