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How to prove that if h(t) hazard function is failure rate function then integration of h(t) from 0 to infinity is infinity .

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The cumulative hazard function $\Lambda(t) = \int_{0}^t h(s) ds$ is related to the survival function by $S(t) = \exp(-\Lambda(t))$. The survival function is cadlag starting at 1 at time 0 and tending to 0 as $t \rightarrow \infty$. Therefore $\Lambda(t) \rightarrow \infty$ as $t \rightarrow \infty$.

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  • $\begingroup$ Thank you , I was thinking the same but wasn't sure, thanks $\endgroup$
    – simran
    Jun 5 '21 at 3:57

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