A Modification of Schwarz's Inequality with Applications to Distributions

Moriguti, Sigeiti

Ann. Math. Statist., Tome 24 (1953) no. 4, p. 107-113 / Harvested from Project Euclid

Résumé

Theorem 1 provides us with a result from which we can derive the modified Schwarz inequality (1.2) or, more generally, (3.8). The formulas hold when $x(t)$ is any nondecreasing function belonging to a certain wide class, and $\bar{\varphi}(t)$ is the right-hand derivative of the "greatest convex minorant" of $\Phi(t)$. The necessary and sufficient conditions for equality to hold are also given. Applications to distribution problems in statistics are discussed in Section 4.

Publié le : 1953-03-14
Classification:

@article{1177729088,
     author = {Moriguti, Sigeiti},
     title = {A Modification of Schwarz's Inequality with Applications to Distributions},
     journal = {Ann. Math. Statist.},
     volume = {24},
     number = {4},
     year = {1953},
     pages = { 107-113},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177729088}
}

Moriguti, Sigeiti. A Modification of Schwarz's Inequality with Applications to Distributions. Ann. Math. Statist., Tome 24 (1953) no. 4, pp.  107-113. http://gdmltest.u-ga.fr/item/1177729088/