I have to find a "99% confidence bound" for a standard deviation. This is not hard. The only question I have is whether this is finding the $\chi^2_{.99}$ value or just the upper bound for the 99% confidence interval (between $\chi^2_{.005}$ and $\chi^2_{.995}$). Any help would be appreciated. Thanks in advanced!
2026-02-23 23:24:46.1771889086
Is a 99% upper confidence bound the upper limit of a 99% confidence interval?
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The upper confidence bound would be the $\chi^2_{0.99}$ value. As a Google seach will show, the term is in fairly common use, and has a standard meaning: "the" point $a$ such that $F_X(a)=0.99$, the point that has $1\%$ of the area in the right tail.
In particular, the $99\%$ upper confidence bound is not the upper limit of a $99\%$ confidence interval with $0.005$ in each tail.
For variance particularly, upper confidence bounds are the usual quantity of interest. One wants protection against the variance being "too large."