Thanks for the PR and the suggestion!

Right-censoring occurs because an observation stops being observed in a study period either due to: the study period ending (administrative censoring) or some other random event (if non-random then use competing risks). What you're referring to is specifically administrative censoring.

The flaw in the original is that the example in parentheses says "(e.g., the marathon runner gives up and does not finish the race)", I agree this is a competing risk (though is still technically right-censoring, CR is just the better modelling paradigm, though technically the example is correct). Therefore a better solution is to update that to "(e.g., the marathon runner trips and sprains their ankle") which is a purely random event. Their hypothetical finish time, $Y$, is unobserved but one could still attempt to predicting this using the standard single-event framework (the purpose of survival analysis).

I'm not adverse to a new example but the example should be general right-censoring not some specific sub-field.

@BjarkeHautop thanks for the suggestion and PR! I edited a bit further the text adding the distinction between random and administrative censoring (+ better examples) which I think is important (as Raphael argued also above).

That sounds like everybody is ok with this PR now? Please confirm before I merge.

@larskotthoff good to merge, I refined it as much as I could!

@be-marc I think this should be good to merge - some account problem seesm to be the failure here, probably because this is from a fork?