Let $f(x)$ and $g(x)$ be two probability density functions. Does the expression:
$ C = 2\int _{-\infty}^{\infty}\left[f(x)\int _{-\infty}^{x}g(y)\,dy\right]\,dx $
have any meaningful graphical representation when $E[Y]>E[X]$, where $X$ has $pdf$ $f(x)$ and $Y$ has $pdf$ $g(x)$? Or, can it be expressed in a simpler fashion?
From some numerical simulations, it seems to approximately describe the "overlap" area of the two $pdf$'s. And if we let $g(x)==f(x)$ then $C$ is close to 1... The overlap is defined as, $\int_{-\infty}^{\infty} \min(f(x),g(x)) dx $