A note on stochastic comparisons of excess lifetimes of renewal processes (Q2774452)

Let \(N\) be a renewal process with interarrival distribution \(F\). For \(t\geq 0\), let \(\gamma(t)\) be the excess lifetime at time \(t\). The authors show that if \(\gamma(t)\) is stochastically decreasing in the Laplace transform order, then \(F\) has some aging property. They also show that if \(F\) has various aging properties, then \(\gamma(t)\) and \(\gamma(0)\) can be compared according to various stochastic orders.