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.