Truncated, Not Censored
Why a truncated unit was never given the chance to be in the sample — and how the likelihood must condition on that
Closes out the incomplete-data trilogy by deriving why truncation is a fundamentally different (and more severe) problem than missing data or censoring: a truncated unit is never in the sample at all. Derives the truncated likelihood f(t)/S(tau), a full worked MLE for a left-truncated Exponential (an insurance-deductible example, using the same memorylessness property from the Exponential and Geometric sheets), and the combined truncation-plus-censoring likelihood for studies with both delayed entry and follow-up censoring. A simulation shows a naive fit that ignores truncation overstates the true mean by 40%.
This article is part of an Analyze subscription.
Subscribe to read Truncated, Not Censored in full, along with every other article in the library.
See plans