Consider harzard ratio $$ H(x) = \frac{f(x)}{1-F(x)} $$ where $f(x),F(x)$ are pdf and cdf of a random variable, respectively.
My question is can $H(x)$ take any form?
In other words, if I'm given an arbitrary function $H(x)$, does there always exist a random variable $X\sim f(x)$, whose harzard ratio is $H(x)$?
Thank you!