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This question was closed as being too vague.

I disagree (and voted to open). I wanted to quickly explain why I think this is a well posed question, or at the least it suggests an important discussion.

Here are ways you could estimate the mean, with discussion. Note that this same argument could be made for right censored data: just replace NPMLE with Kaplan Meier curves (for those not so familiar with interval censored terminology).

1.) One way to estimate the mean is from parametric models. This of course includes strong modeling assumptions, which may lead to less obvious bias from outliers than in a traditional mean of samples approach.

2.) We could also use the the NPMLE to compute the mean. But this is a really bad idea if we have right censoring in our data. The NPMLE will put zero mass beyond the last known point, which can greatly bias the mean with right skewed data/high censoring rates. Similarly, there is a special case in which the mean of the NPMLE isn't even defined (i.e., when there is a right censored value whose limit is greater than the largest known event time).

As such, the method I would endorse would be to estimate with a a parametric model, then inspect the model fit using the NPMLE.

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    $\begingroup$ You've in effect written a much better question, which you might well post on CV itself. I didn't see it earlier, but I don't think the original question is a good one. It ends up focused on what to do in R, which is also off-topic. There is a statistical core, but it's not made a good question just because someone like yourself can imagine a better one. $\endgroup$
    – Nick Cox
    Apr 4, 2020 at 11:56

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