One of the reasons that I cover duration models in my graduate applied econometrics course, even though they are not used that widely in the literature (other than, oddly, in the Netherlands and Denmark) is so that I can cover length-biased sampling.
If you take a random section of spells - hospital stays, welfare receipt, marriage or whatever - you will over-sample long spells relative to their proportion of all spells because they are more likely to be in progress at the time you draw your sample.
The duration literature calls this length-biased sampling and it is another manifestation of the same basic point rediscovered in this column in the Guardian, which explains why your friends will, on average, have more friends than you do, and why, on average, you will be less fit than the other people at your gym (if you have a gym).
Hat tip: Good s**t blog
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