
Hazard Function Question
I am trying to show that the hazard function h(t)=d/dt(ln(R(t))) is constant if and only if the variable has an exponential distribution where R(t) is the reliability 1F(t) of a random variable with cdf F. I am not totally sure where to start in order to prove this in either direction.
Is it right to simplify to h(t)=F'(t)/(1F(t)) and plug in?

Okay, so given that it is an exponential distribution, I can prove that the hazard is constant, since I know the cdf and pdf of an exponential:
$\displaystyle \frac{R'(t)}{R(t)}=\frac{R(t)}{1(1exp(xt))}=\frac{F'(t)}{exp(xt)}=\frac{x*exp(xt)}{exp(xt)}=x$
However, can someone help with how to prove in the other direction. i.e. how to show that given that the reliability of a random variable with cdf F is defined to be $\displaystyle R(t)=1F(t)$ and that the hazard is $\displaystyle h(t)=\frac{d}{dt}(ln(R(t)))$ that this implies the hazard of the variable is constant only if the variable is exponential?
EDIT: Nevermind, I solved it.