Number 26/Measurement & inference/Risk
The Tail Omission Factor
The quantity
The ratio of the true maximum of a distribution to the maximum observed in a record of given length, as a function of tail heaviness.
01Why it matters
It quantifies how much a record understates extremes, which is the number that should sit beside every return-period estimate.
02Expected value
Well above one for heavy tails, close to one for thin tails, and rising with record length only slowly.
03How it would be measured
Estimate tail index from the record, then compute the expected ratio analytically.
04What would refute it
If observed maxima track true maxima regardless of record length, the factor is one.