Suppose $x_1, \cdots, x_n$ are the order-statistics of a random sample from a distribution $F$. We assume that the expectations $\xi_{i:n} = E(x_i)$ are known, and derive sharp bounds on $F(x)$ for all $x$. These results are obtained by transforming the problem into a classical one involving ordinary power moments.
Publié le : 1973-04-14
Classification:
Inequalities,
distribution functions,
order statistics,
Chebyshev,
62G30,
60E05,
26A87
@article{1176996981,
author = {Mallows, C. L.},
title = {Bounds on Distribution Functions in Terms of Expectations of Order- Statistics},
journal = {Ann. Probab.},
volume = {1},
number = {5},
year = {1973},
pages = { 297-303},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996981}
}
Mallows, C. L. Bounds on Distribution Functions in Terms of Expectations of Order- Statistics. Ann. Probab., Tome 1 (1973) no. 5, pp. 297-303. http://gdmltest.u-ga.fr/item/1176996981/