How do I show the following: Suppose $\lambda=-\frac{S'(x)}{S(x)}$, where $S(x)=1-F(x)$ is survival probability. Show that $\lambda$ is the intensity of the exponential distribution with cdf $F(x)=1-e^{-\lambda x}$.

  • 1
    $\begingroup$ I think the way the question is worded is awkward. I would have said: Suppose the intensity function defined by $\lambda(x)=\frac{S^{'}(x)}{S(x)}$ is equal to a constant $\lambda$. Show that in this case the cdf of the distribution is the cdf of an exponential, which is $F(x)=1-e^{-\lambda x}$. And you verify this by plugging in the $F(x)$ in the previous expression and seeing that you do indeed get a constant. $\endgroup$
    – Alex C
    Jul 16, 2017 at 17:40

1 Answer 1


You didn't define an intensity function, and you might be assuming what's to be shown. Does this help? \begin{align*} -\frac{S'(x)}{S(x)} &= \lambda\frac{e^{-\lambda x}}{e^{-\lambda x} } \tag{defn of survival function} \\ &= 1. \end{align*}


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.