On the inference for the two-parameter exponential distribution

On the inference for the two-parameter exponential distribution

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Article ID: iaor19881278
Country: Japan
Volume: 54
Issue: 2
Start Page Number: 17
End Page Number: 35
Publication Date: Jul 1988
Journal: Journal of Economics
Authors:
Keywords: distribution, testing, statistics: general
Abstract:

The author discusses the inference of parameter (θ1,θ2) of two-parameter exponential distribution, where θ1 and θ2 are the location parameter and the scale parameter, respectively. First he derives the (natural) conjugate family of two-parameter distribution and proves nine propositions concerning conjugate distributions. These propositions are utilized for the inference. Next, the posterior distribution of (θ1,θ2) is derived for a conjugate prior distribution and the observed value. As usual, this also belongs to the conjugate family. The inference (interval estimate, point estimate and test of hypotheses) concerning θ1 (or θ2) is shown on the basis of the marginal posterior distribution of θ1 (or θ2). Further, the simultaneous inference of θ1 and θ2 is shown. Finally, the sequential inference (sequential estimation and sequential test of hypotheses) for two-parameter exponential distribution is discussed and reasonable stopping rules are proposed. [In Japanese.]

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