<p>This <a href="https://stats.stackexchange.com/q/458277/76981">question</a> was closed as being too vague. </p>

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

<p>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). </p>

<p>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. </p>

<p>2.) We could also use the the NPMLE to compute the mean. But this is a <strong>really</strong> bad idea if we have right censoring in our data. The NPMLE will put zero mass beyond the last <em>known</em> point, which can <strong>greatly</strong> 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). </p>

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