Let $p_\nu(t, \delta)$ be the density at $t$ of a noncentral $t$-variable with $\nu$ degrees of freedom and noncentrality parameter $\delta$. It is proved that for any $d > 0$ and fixed $t, p_\nu(t, \delta + d)/p_\nu(t, \delta)$ is a strictly decreasing function of $\delta$.
Publié le : 1983-09-14
Classification:
Noncentral $t$,
density ratio,
monotonicity,
noncentrality parameter,
62E99,
62L10,
33A65
@article{1176346269,
author = {Wijsman, Robert A.},
title = {Monotonicity in the Noncentrality Parameter of the Ratio of Two Noncentral $t$-Densities},
journal = {Ann. Statist.},
volume = {11},
number = {1},
year = {1983},
pages = { 1008-1010},
language = {en},
url = {http://dml.mathdoc.fr/item/1176346269}
}
Wijsman, Robert A. Monotonicity in the Noncentrality Parameter of the Ratio of Two Noncentral $t$-Densities. Ann. Statist., Tome 11 (1983) no. 1, pp. 1008-1010. http://gdmltest.u-ga.fr/item/1176346269/