How do we prove that the failure rate function $\displaystyle r(t) = \frac{f(t)}{1-F(t)} $ uniquely determines the distribution $\displaystyle F $? I wrote $\displaystyle r(t) = \frac{\frac{d}{dt} F(t)}{1-f(t)} $.
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?? Why did the denominator change? Can't you just solve for F? Consider R(t) = ln(1-F(t)) with r(t) = R'(t).
typo
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