Confidence Interval and EstimatedDistribution

Is there an easy way of obtaining a confidence interval directly from EstimatedDistribution?

In NonLinearModelFit there’s the MeanPredictionBands and the ParameterConfidenceIntervalTable.
There are still, also, the MeanCI and VarianceCI functions available.

But how to easily implement a CI analysis, on a distribution fitted by EstimatedDistribution (or FindDistributionParameters)?

I (finally) found the same question on Mathematica.SE:

You can also consider using R’s fitdistr() or mle() functions through RLink, though resorting to an external system is not the most convenient or pleasant way …