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In this paper, we develop the noninformative priors for the linear combinationsof means in the exponential distributions. We develop the matching priors and thereference priors. The matching priors, the reference prior and Je reys’ prior for thelinear combinations of means are developed. It turns out that the reference prior andJe reys’ prior are not a matching prior. We show that the proposed matching priormatches the target coverage probabilities much more accurately than the referenceprior and Je reys’ prior in a frequentist sense through simulation study, and an examplebased on real data is given.Keywords: Linear combinations of means, matching prior, reference prior. 1. Introduction The exponential distribution plays an important role in the eld of reliability. The useful-ness of the exponential distribution in reliability applications can be found in the early workof Davis (1952), Epstein and Sobel (1953), and others. Further justi cation, in the form oftheoretical arguments to support the use of the exponential distribution as the failure law ofcomplex equipment, is presented in the book by Barlow and Proschan (1975) and Lawless(2003).A problem of making inference about the linear combination of exponential means occurswhen calculating the di erence of two exponential life times, comparing the di erence oftwo quantiles, estimating the reliability of the series system, comparing contrasts of themeans, and estimating of the common mean. The mentioned quantities are expressed bythe linear combination of means. Once statistical inference for linear combination of meansis developed, the statistical inferences mentioned above can be dealt by simply insertingconstants.

Noninformative priors for linear combinations of exponential means