In statistics, truncation results in values that are limited above or below, resulting in a truncated sample.[1] A random variable is said to be truncated from below if, for some threshold value , the exact value of is known for all cases , but unknown for all cases . Similarly, truncation from above means the exact value of is known in cases where , but unknown when .[2]
Truncation is similar to but distinct from the concept of statistical censoring. A truncated sample can be thought of as being equivalent to an underlying sample with all values outside the bounds entirely omitted, with not even a count of those omitted being kept. With statistical censoring, a note would be recorded documenting which bound (upper or lower) had been exceeded and the value of that bound. With truncated sampling, no note is recorded.
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