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What is the definition of a hazard rate? What is a hazard function?

I thought it was the probability that a unit does not survive the time period conditional on being alive, but I see hazard rates above one when I compute hazard rates myself and in examples of survival analysis (e.g. p.10 of http://courses.washington.edu/b515/l16.pdf). How can the hazard rate be above one if it is a probability?

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It is the expected number of times you are expected to experience the event per time interval given that you have survived thus far. The key difference with your definition is that it is a rate not a probability.

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    $\begingroup$ Oh, that makes much more sense. What if I want to limit the event to happening once? Do I need to use a special kind of survival analysis? And/or can I compute the probability the event happens? Does that quantity have a name? $\endgroup$ – user7340 Oct 29 '14 at 15:37
  • $\begingroup$ @user7340: (1) Imagine when you die you're immediately resurrected, without being rejuvenated, & are once again at risk. It's not necessary to believe that to be a realistic scenario to employ the concept of hazard. (2) The probability at birth that you die between any specified ages is the difference in the values of the lifetime distribution function at those ages; the probability that you die in the next year is the difference in the values of the lifetime distribution functions now & one year from now divided by the value of the survival function now; the probability that you die is 1. $\endgroup$ – Scortchi - Reinstate Monica Oct 29 '14 at 16:11

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