# Failure Rate Function-Stats

• January 28th 2008, 12:46 PM
shilz222
Failure Rate Function-Stats
How do we prove that the failure rate function $r(t) = \frac{f(t)}{1-F(t)}$ uniquely determines the distribution $F$? I wrote $r(t) = \frac{\frac{d}{dt} F(t)}{1-f(t)}$.
• January 28th 2008, 01:52 PM
TKHunny
?? Why did the denominator change?

Can't you just solve for F?

Consider R(t) = ln(1-F(t)) with r(t) = R'(t).
• January 28th 2008, 08:33 PM
shilz222
typo