Let x(1), x(2), …, x(n) be the order statistics of a sample of size n from the exponential distribution with an unknown location-scale parameter (μ,σ). It is shown that usual confidence intervals for σ based on the only statistic Σn__<i=1>(x(i)-x(1)) can be improved by using the statistic x(1). Further the degree of the improvement is computed numerically.
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