f**********g
发帖数: 107 | 1 Let x(1),...,x(n) be order statistics drawn from an arbitrary distribution X
, where x(n) is the largest one.
Y is an arbitrary distribution independent with X.
Let Z=X+Y, and z(1),...,z(n) be order statistics drawn from Z.
我们能不能证明the expect value of z(n)-z(n-1) is greater than the expect
value of x(n)-x(n-1), namely, E[z(n)-z(n-1)]>E[x(n)-x(n-1)].
也就是说当加上一个independent variable以后，first order statistic和second
order statistic之差是否变大了呢？ | t**o
发帖数: 338 | 2 intuitively, I don't think it is true. You can run a numerical simulation to
check. | f**********g
发帖数: 107 | 3 I have run a lot of simulations. All results were consistent with this
argument. | U*****e
发帖数: 2882 | 4 I think you conjecture is possible. A simple example is rv X being
degenerated and any rv Y can work like a spreading effect.
But I have not found the proof. |
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