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...

Unlike stochastic ordering ([greater-or-equal, slanted]st), which is preserved under convolution (i.e., summation of independent random variables), so far it is only known that likelihood ratio ordering ([greater-or-equal, slanted]lr) is preserved under convolution of log-concave (PF2) random...

A representation, called the total hazard construction, of dependent random variables by means of independent exponential random variables is studied. Conditions which imply association of nonnegative random variables are found using this construction. Furthermore, new conditions which imply...