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Fixed width confidence intervals for the location parameter of an exponential distribution. (English) Zbl 0559.62030
Let \(f_{\theta,\sigma}(x)=\sigma^{-1}e^{-(x- \theta)/\sigma}I_{(x\geq \theta)}\). The authors study fixed width confidence intervals for \(\theta\), when \(\sigma\) is not known. The paper has two parts. In the first part, the authors obtain second order results, as \(d\to 0\), for the expected sample size and coverage probability. For the estimate proposed by N. Mukhopadhyay [Bull., Calcutta Stat. Assoc. 23, 85-95 (1974; Zbl 0342.62058)] Monte-Carlo results are also presented to elucidate the results.
In the second part, the authors construct confidence intervals of width d and coverage probability 1-\(\alpha\). They then study the asymptotic behaviour of the expected sample size as \(d\to 0\) and also as both d and \(\alpha\) go to 0.
Reviewer: R.V.Ramamoorthi

62F25 Parametric tolerance and confidence regions
62E20 Asymptotic distribution theory in statistics
62L12 Sequential estimation
Full Text: DOI
[1] Anscombe, F.J. Large sample theory of sequential estimation. Proc. Cambridge Phil.Soc. Vol. 48, pp.600–607. · Zbl 0047.13401
[2] Bickel P.J., Ann. Math. Statist 36 pp 457– (1968)
[3] Lombard F., S. Afr. Statist. J 12 pp 1– (1978)
[4] Mukhopadhyay N., Calcutta Statist. Assoc. Bul 23 pp 85– (1974)
[5] Simons G., Ann. Math. Statist 39 pp 1946– (1968) · Zbl 0187.15805
[6] Starr, N. and Woodroofe, M. Remarks on a stopping time. Proc. Nat.Aoad.Sci. Vol. 61, pp.1215–1218. · Zbl 0193.47002
[7] Woodroofe M., Ann. Statist 5 pp 984– (1977) · Zbl 0374.62081
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