Abstract: In this talk, I shall define two types of hybrid censoring and motivate their use. Then, I shall illustrate these concepts by considering an exponential distribution and deriving  the maximum likelihood estimates of the mean lifetime under the two types of hybrid censoring. Then, I will use the conditional  moment generating function approach to derive the exact distributions of these MLEs and the confidence intervals obtained from them. Finally, I will take some examples to illustrate these results.

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