Abstract
Censored data occur when the value of an observation is only partially known. For example, it may be known that someone’s exact wealth is unknown but it may be known that their wealth exceeds one million dollars. In left censoring, the data may fall below a certain value whereas in right censoring, it may be above a certain value. Type I censoring occurs when the subjects of an experiment are right censored. Type II censoring occurs when the experiment stops after a certain number of subjects have failed; the remaining subjects are then right censored. Truncated data occur when observations never lie outside a given range. For example, all data outside the unit interval is discarded. A good example to illustrate the ideas occurs in insurance companies. Left truncation occurs when policyholders are subject to a deductible whereas right censoring occurs when policyholders are subject to an upper pay limit.
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Notes
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In fact, Gehan introduced a further refinement depending on whether the larger observation is censored or not.
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Alvo, M., Yu, P.L.H. (2018). Analysis of Censored Data. In: A Parametric Approach to Nonparametric Statistics. Springer Series in the Data Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-94153-0_12
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