Multivariate aging properties of epoch times of nonhomogeneous processes (Q1873115)

For a nonnegative random vector \(\mathbf T\) the classes ``multivariate Polya frequency of order 2'' (\(\text{MPF}_2\)) and ``multivariate increasing failure rate'' (MIFR) are introduced. For the case that \(\mathbf T\) denotes the first epoch times of a nonhomogeneous Poisson process or a nonhomogeneous pure birth process conditions on the processes are derived that \(\mathbf T\) is either \(\text{MPF}_2\) or MIFR. The results are illustrated by assuming a generalized Yule birth process and by considering a random vector of generalized order statistics.