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The conditional confidence interval for the location parameter of an exponential distribution following a preliminary test is investigated. The conditional confidence interval (CCI) may be shorter than the unconditional confidence interval (UCI) in contrast to the findings for the mean of a normal distribution by Meeks and D'Agostino (1983). The conditional coverage probability of the UCI is obtained by computing the coverage probability under the conditional probability density function. It is shown that the conditional coverage probability of the UCI is not uniformly greater than or less than the nominal level.
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Chiou et al. (1995) studied this question.
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