| Abstract: | Abstract There are given k (≥22) independent distributions with c.d.f.'s F(x;θj) indexed by a scale parameter θj, j = 1,…, k. Let θi] (i = 1,…, k) denote the ith smallest one of θ1,…, θk. In this paper we wish to show that, under some regularity conditions, there does not exist an exact β-level (0≤β1) confidence interval for the ith smallest scale parameter θi based on k independent samples. Since the log transformation method may not yield the desired results for the scale parameter problem, we will treat the scale parameter case directly without transformation. Application is considered for normal variances. Two conservative one-sided confidence intervals for the ith smallest normal variance and the percentage points needed to actually apply the intervals are provided. |
