On Variant Confidence Intervals for the Parameters of a New Life Distribution
ROCKETDYNE CANOGA PARK CA
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In this paper the problem of obtaining confidence intervals and tests of hypotheses for the parameters of a new distribution derived by Birnbaum and Saunders is explored. The maximum-likelihood estimators of the shape and scale parameters are investigated and shown, for samples of size two, to be such that they cannot provide invariant confidence intervals for either of the parameters. A statistic which is asymptotically independent of the shape parameter alpha is shown to be capable of providing confidence bounds for the scale parameter beta. These bounds, however, are subsequently shown to exhibit invariance with respect to alpha only for samples of size fifty or larger. Finally, three statistics based on maximal invariants for tests and confidence sets independent of alpha are investigated in terms of accuracy of confidence bounds for power of tests concerning beta. Percentage points of the statistics yielding the most accurate confidence bounds for beta, among those investigated, are tabulated for samples of size n, n 215.
- Statistics and Probability
- Manufacturing and Industrial Engineering and Control of Production Systems