Showing papers by "Albert W. Marshall published in 1986"

Multivariate New Better than Used Distributions

Abstract: A general theory of multivariate new better than used NBU distributions is developed. Using the general theory some multivariate NBU conditions are introduced and studied. Some of the results apply as well to multivariate increasing hazard rate average IHRA and exponential distributions. Proofs of some related well-known implications are simplified.

NBU Processes with General State Space

Abstract: Waiting times for many kinds of events can be represented as first passage times for appropriate stochastic processes. In some applications the most natural stochastic process is multidimensional. In other applications it may be more natural to consider a stochastic process which takes on values in a more general space. In this paper we consider new better than used NBU stochastic processes on partially ordered separable Banach spaces, that is processes which have NBU first passage times to closed upper sets. Various equivalent conditions for a process to be NBU are derived. Some of the results can be used also to characterize increasing hazard rate average IHRA processes. Examples of such processes include processes with shocks and recovery and processes with random repair times. Some applications in reliability theory and in other areas of probability are given.

Multivariate new better than used distributions: a survey

Abstract: Various multivariate NBU (new better than used) notions are surveyed in this paper. The relationships among them are studied. Some preservation properties of these notions under different kinds of operations are listed and open questions are indicated. Multivariate NBU distributions with exponential marginals are discussed. Finally some examples are given.