Dispersion measures and dispersive orderings

Dispersion measures and dispersive orderings

In this paper, the comparison of random variables according to the functionals of a general class of dispersion measures is characterized in terms of the dilation order. The Gini’s mean di¤erence is a particular member of this general class. In addition, a new and weaker order, called the second-order absolute Lorenz ordering, is introduced, and we judge random variables according to certain fu...

Characterizations of Inequality Orderings by Means of Dispersive Orderings

The generalized Lorenz order and the absolute Lorenz order are used in economics to compare income distributions in terms of social welfare. In Section 2, we show that these orders are equivalent to two stochastic orders, the concave order and the dilation order, which are used to compare the dispersion of probability distributions. In Section 3, a sufficient condition for the absolute Lorenz o...

Measures of Central Tendency and Dispersion.

Comparing Variances and Other Measures of Dispersion

Testing hypotheses about variance parameters arises in contexts where uniformity is important and also in relation to checking assumptions as a preliminary to analysis of variance (ANOVA), dose-response modeling, discriminant analysis and so forth. In contrast to procedures for tests on means, tests for variances derived assuming normality of the parent populations are highly nonrobust to nonno...

Octave spanning wedge dispersive mirrors with low dispersion oscillations.

A novel concept for octave spanning dispersive mirrors with low spectral dispersion oscillations is presented. The key element of the so-called wedge dispersive mirror is a slightly wedged layer which is coated on a specially optimized dispersive multilayer stack by a common sputter coating process. The group delay dispersion (GDD) of a pulse reflected on a wedge dispersive mirror is nearly fre...