Confidence Intervals for the Weibull distribution

Comparing the lengths of non-symetric CI’s with that of the symmetric CI of the same level of confidence.

Select the level of confidence $(1-a)*100$ by chosing the value of $a$. Select the value of the shape parameter $k$ of the Weibull 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 on the left is the difference $j-i$ 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. That is particularly noticeable when the skewness of the distribution is larger i.e. for $k$ close to $1$.

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