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TESTING HYPOTHESES ABOUT THE POWER LAW PROCESS

UNDER FAILURE TRUNCATION

USING INTRINSIC BAYES FACTORS

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RAMA T. LINGHAM^{1} AND S. SIVAGANESAN^{2}

^{1} *Division of Statistics, Northern Illinois University, DeKalb, IL 60115-2854, U.S.A.*

^{2} *Department of Mathematical Sciences, University of Cincinnati,*

Old Chemistry Building (ML25), Cincinnati, OH 45221-0025, U.S.A.
(Received February 7, 1996; revised October 3, 1996)

**Abstract.**
Conventional Bayes factors
for hypotheses testing cannot typically
accommodate the use of standard noninformative
priors, as such priors are defined only up to
arbitrary constants which affect the values of
the Bayes factors. To circumvent this problem,
Berger and Pericchi (1996, * J. Amer.
Statist. Assoc.*, **91**, 109-122)
introduced a new criterion called the Intrinsic
Bayes Factor (IBF). In this paper, we use
their methodology to test several hypotheses
regarding the shape parameter of the power law
process. Assuming that we have data from the
process according to the failure-truncation
sampling scheme, we derive the arithmetic and
geometric IBF's using the reference priors. We
deduce a set of intrinsic priors that correspond
to these IBF's, as the observed number of
failures tends to infinity. We then use these
results to analyze an actual data set on the
failures of an aircraft generator.

*Key words and phrases*:
Automatic
Bayes factor, Intrinsic Bayes factors,
(non-homogeneous) Poisson process, reference
prior, repairable systems, tests of hypotheses,
Weibull process.

**Source**
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