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

March 17, 2014

(This article was originally published at The Chemical Statistician » Statistics, and syndicated at StatsBlogs.)

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!