Studying the joint distributional properties of partial sums of independent random variables, we obtain stochastic analogues of some simple deterministic results from the theory of majorization, Schur-convexity, and arrangement monotonicity. More explicitly, let Xi([theta]i), i =1, ..., n, be...

The supermodular and the symmetric supermodular stochastic orders have been cursorily studied in previous literature. In this paper we study these orders more thoroughly. First we obtain some basic properties of these orders. We then apply these results in order to obtain comparisons of random...

The properties of IFR (increasing failure rate) and PF2 (Polya frequency of order 2) are of use and importance in the study of univariate random lifetimes in reliability theory. In this paper these notions are extended to the multivariate setting. The extensions are not just technical, but they...

Consider the lifelengths T1,..., Tk of k components subjected to a randomly varying environment. They are dependent on each other because of their common dependence of the environment. The parameters of the model are the distribution of the random process which describes the environment and a...

A discrete time stochastic process {Xn, N = 0, 1, 2, ...} is said to be temporally convex (concave) if E[theta](Xn) is a nondecreasing convex (concave) function of n whenever [theta] is a nondecreasing convex (concave) function. Similarly one can define temporal convexity and concavity for...