A probability inequality for ranges and its application to maximum range test procedures |
| |
Authors: | Prof Dr T Royen |
| |
Institution: | (1) Fachhochschule Rheinland-Pfalz, Abteilung Bingen, Rochusallee 4, D-6530 Bingen |
| |
Abstract: | Summary It is proved that for any fixed argument the sequence (P
k) of the distribution functions of the ranges ofk i.i.d. univariate random variables is log-concave if the random variables have a log-concave density. If the support of the
distribution is an infinite interval and the density is monotonous then the theorem holds also with “log-convex” instead of
“log-concave”. The resulting inequalities can be used by a quick algorithm for closed maximum range test procedures for all
pairwise comparisons (Royen 1988, 1989a, 1989b). Under the above assumptions the application of this algorithm can be extended
e.g. to pairwise comparisons of variances. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|