TITLE: Modeling question: how often does "the world's oldest person" die?
QUESTION [38 upvotes]: This story yesterday (no need to follow the link to understand the question!)
http://www.cnn.com/2011/US/02/01/texas.oldest.person.dies/index.html?hpt=T2
reminds me that I've often wondered about the following:
Suppose you have a fixed mortality curve $f(x)$ expressing the probability of a person's remaining alive at age $x$.  Suppose also, for simplicity, you have a steady state population, so a given fixed birth rate.  How would one compute from $f(x)$, and the birth rate, the probability distribution $\rho$ governing the time intervals from one "world's oldest person dies" event to the next?
Actually though I think I could probably write down explicit integrals to answer my own question literally, but I don't expect they would say much as such.  So I'm really looking for a softer answer that would explain what features of $f(x)$, what measures of the heaviness of its tail I guess, dominate the behavior of $\rho$ and how?

REPLY [4 votes]: There was a discussion on this quite a long time ago at sci.mat. See: 
http://groups.google.com/group/sci.math/browse_thread/thread/531c39a2e5723df8/528137c752566266?lnk=gst&q=oldest+person#528137c752566266