This exercise would, in general, reduce the number of observations above and below the threshold equally. In this case, while we would be able to estimate the threshold with less precision, the expected point estimate would remain unchanged. Now consider a case where the probability of observing a plan of sufficient quality were small, say five percent. Each high-quality draw is particularly important in identifying the threshold. Moreover, each such draw is from the
tail of the distribution, which in turn teaches us about the extent of this tail. Since the likelihood of observing extreme observations is low, we will infer that the ones we do observe are the most extreme, and systematically underestimate the size of the tail.