Generalization of the \(\mathfrak {L}\)-property of the distribution function (Q1842449)

Multidimensional analogs of ``New Better (Worse) than Used on Average'' distributions (abbreviated respectively as NBUA or NWUA) were introduced by the author in ibid. 28, No. 2, 170-179 (1992); translation from Kibern. Syst. Anal. 1992, No. 2, 12-23 (1992), on the basis of the multivariate distribution function of the remaining life. In comparison with the purely mechanical extension of the NBUA property to the multidimensional case, our approach has definite advantages: it can be used to analyze multivariate distribution functions for membership in the corresponding classes and check for preservation of the main reliability operations; it maintains an obvious interrelationship with various objects of probability theory, such as multidimensional renewal processes, branching processes, and stopping processes. Here, we continue the study of ``aging'' distributions, which are more general than NBUA and NWUA.