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...
Giuseppe
=================================================================
Instructions for joining and leaving this list and remarks about
the problem of INAPPROPRIATE MESSAGES are available at
http://jse.stat.ncsu.edu/
=================================================================
