-1
$\begingroup$

How do you simulate an exponential random variable over an interval $[0, T]$ with $T > 0$?

$\endgroup$
  • 1
    $\begingroup$ Do you know mathematics stack exchange ? $\endgroup$ – MJ73550 Dec 17 '16 at 21:24
3
$\begingroup$

You should post on mathematics.stackexchange

I answer but I should not.

Let $X $ be an exponential r.v. of parameter $\lambda $ $$P (X<u|X <T)=\frac {P (X<min (u,T))}{P (X <T )} $$ So for $0\leq u\leq T$ $$P (X<u|X <T)=\frac {1-\exp (-\lambda u)}{1-\exp (-\lambda T)} $$

So if $U $ is an uniform on $ [0,1]$ then $$Y= -\frac {1}{\lambda }\ln\left (1-U (1-\exp(-\lambda T))\right) $$ is an exponential r.v. of parameter $\lambda $ conditionned to be on $[0,T] $

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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