Video Tutorial – The Hazard Function is the Probability Density Function Divided by the Survival Function

In an earlier video, I introduced the definition of the hazard function and broke it down into its mathematical components.  Recall that the definition of the hazard function for events defined on a continuous time scale is

h(t) = \lim_{\Delta t \rightarrow 0} [P(t < X \leq t + \Delta t \ | \ X > t) \ \div \ \Delta t].

Did you know that the hazard function can be expressed as the probability density function (PDF) divided by the survival function?

h(t) = f(t) \div S(t)

In my new Youtube video, I prove how this relationship can be obtained from the definition of the hazard function!  I am very excited to post this second video in my new Youtube channel.  You can also view the video below the fold!

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2 Responses to Video Tutorial – The Hazard Function is the Probability Density Function Divided by the Survival Function

  1. skaae says:

    Thanks for the explanation. The first time someone explained what appears to be a fact in most text books! I suggest you break down the partial likelihood in Cox models as well :)

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