Giuseppe Andrea Paleologo wrote:
>
> I am dealing with a simple conjecture. Given two generic positive random
> variables, is it always true that the sum of the quantiles (for a given
> value p) is greater or equal than the quantile of the sum?
>
> In other words, let X, Y be positive random variables with continuous
> but arbitrary joint CDF F(x,y), and let Z = X + Y, with CDF Fz(z). Let
> Fx(x) and Fy(y) are the marginal CDFs for X and Y respectively. Is it
> true that
>
> Fx^-1 (p) + Fy^-1 (p) >= Fz^-1(p)
>
> with 0 < p < 1 ?
>
> Any insight or counterexample is greatly appreciated. I am sure this is
> proved in some textbook, but independently from that, I think this
> should be doable via elementary methods...
>
I'm sure I've seen it somewhere.
It seems obvious for well-behaved cases, and I assume it is true in
general,
but I must admit my brain is completely not in gear at the moment.
Glen
=================================================================
Instructions for joining and leaving this list and remarks about
the problem of INAPPROPRIATE MESSAGES are available at
http://jse.stat.ncsu.edu/
=================================================================
