I am trying to calculate confidence intervals for a complicated statistic that follows an asymmetric, non-negative, distribution. The statistic is heavily skewed from 0 to 1 but technically goes to positive infinity, kind of similar to an odds ratio.

My question is, is it ok to use a percentile confidence interval for this statistic? I assume it might not be appropriate because of the skewed distribution, and I can't just log transform the variable or anything because it's still preserving the order of the values so will still be skewed. I have read about things like BCa intervals, but not sure if that's appropriate here. I was hoping for any sort of advice or literature on potentially how to proceed or anything thoughts at all.

Edit: I apologize if this is not the correct way to edit the question with additional information. I don't want to get into too much detail here, but basically, I am calculating an index (the Chou-Talalay Combination Index) that describes the how two chemicals interact with one another in combination.

It is essentially the summation of fractions of chemical concentrations. Each fraction consists of the concentration of a given chemical used in your experiment to some theoretically necessary concentration. The index is null at the value of 1, so values below 1 are considered to show synergy among the various chemicals and values above 1 are considered to show antagonism.

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    $\begingroup$ Can you give some context and details? And, confidence intervals are for parameters, not statistics, so please specify what parameter you are estimating. Also see stats.stackexchange.com/questions/186957/…, stats.stackexchange.com/questions/365208/… $\endgroup$ Commented Apr 17, 2020 at 15:36
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    $\begingroup$ The 'boot' R package is very nice and reports four different confidence intervals for population parameters of interest via the function 'boot.ci': (1) the normal interval, (2) the basic interval, (3) the percentile interval and (3) the BCa interval. I would report all 4, so long as the interval endpoints are physically sensible (e.g., strictly positive and bounded) $\endgroup$ Commented Apr 17, 2020 at 15:36


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