It is well known that the smaller and the larger of a random sample of size two are positively correlated. The coefficient of correlation is at most one-half, and the upper bound is attained only for rectangular distributions.
Publié le : 1983-08-14
Classification:
Rectangular distribution,
uniform distribution,
order statistics,
Legendre polynomials,
coefficient of correlation,
60E15,
62E10
@article{1176993533,
author = {Terrell, George R.},
title = {A Characterization of Rectangular Distributions},
journal = {Ann. Probab.},
volume = {11},
number = {4},
year = {1983},
pages = { 823-826},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993533}
}
Terrell, George R. A Characterization of Rectangular Distributions. Ann. Probab., Tome 11 (1983) no. 4, pp. 823-826. http://gdmltest.u-ga.fr/item/1176993533/