I was solving a problem and encountered the following:
\sum (f(x)/x) (F(x)/(1-F(x))
Here f(x) is pmf and F(x) is CDF. Is expected value of F(x)/x(1-F(x)) a known function? I found out that f(x)/(1-F(x)) is called hazard function. Also, x is defined over positive values. It can be assumed that x is bounded between two values Xmin and Xmax.
I want to know more about characteristics of this expected value, is it bounded if we take sum until F(x) < 1?
I would appreciate if someone could help me understand this better.