Confidence Intervals of Minimal Length for the F Distribution
We minimise the lengths of confidence intervals of a given level of confidence by varying the tail probabilities ratio.
Select the level of confidence $(1-a)*100$ by chosing the value of $a$. Select the two values of the degrees of freedom, $n$ for the numerator and $m$ for the denominator of the F-distribution. The symmetric CI has equal probability of the left and right tails. By varying the slider $b$ one can visualise the CI having left tail of probability $b*a$ and right tail of probability $(1-b)*a$.
The difference displayed at the top is the difference $t-s$ between the likelihood values at the right endpoint and that at the left endpoint of the current CI. The ratio displayed is calculated between the length of the current CI and that of the symmetric CI. One can verify that the CI is of minimal length exactly when the difference of likelihoods is null.
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