The idea for this book came from the time the authors spent at the Statistics and Applied
Mathematical Sciences Institute (SAMSI) in Research Triangle Park in North Carolina …

In this chapter we study stochastic orders that compare the “location” or the “magnitude” of
random variables. The most important and common orders that are considered in this …

Let X and Y be two random variables with finite expectations EX and EY, respectively. Then
X is said to be smaller than Y in the dilation order if E [ϕ (X-EX)]≤ E [ϕ (Y-EY)] for any …

It is shown, in this note, that the right spread order and the increasing convex order are both
preserved under the taking of random maxima, and the total time on test transform order and …

The equilibrium distribution arises as the limiting distribution of the forward recurrence time
in a renewal process. The purpose of this article is to study the relationships between the …

The purpose of this paper is to study new notions of stochastic comparisons and aging
classes based on the Laplace transform order of residual lives. We give relationships to …

The purpose of this paper is to give a characterization of a new variability order called the
right spread order. This characterization is given in terms of the increasing convex order …

Although the shape of the failure rate function plays an important role in repair and
replacement strategies, the mean residual life (mrl) function is more relevant as the latter …

In this paper, we propose a general frailty model and develop its properties including some
results for stochastic comparisons. More specifically, our main results lie in seeing how the …

Stimulated by the need of describing useful notions related to information measures, we
introduce the 'pdf-related distributions'. These are defined in terms of transformation of …