for example, x is random variable, f(x) and g(x) are two "very very" different distribution functions. It is **impossible** to calculate variance **analytically**, so if we want to compare var(f) and var(g), what are the potentially possible methods?

maybe, sometimes, we know some other information, such as convexity,slope of the function f and g, etc. what we can do?

are there some applied probability papers? I know this is a very simple question:)

thanks a lot.