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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

##### MSC:
 62F25 Parametric tolerance and confidence regions 62E20 Asymptotic distribution theory in statistics 62L12 Sequential estimation
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##### References:
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