On closure of the IFR(2) and NBU(2) classes (Q2731165)

A positive random variable \(X\) is said to be IFR(2) if \(X_{t_1} \geq_{\text{icv}}X_{t_2}\) for all \(0\leq t_1\leq t_2\), where \(\leq_{\text{icv}}\) denotes the increasing concave stochastic order, and \(X_t\) denotes a random variable that is distributed as \(X-t\) given that \(X>t\). The random variable \(X\) as above is said to be NBU(2) if \(X_0\geq_{\text{icv}}X_{t_2}\) for all \(t\geq 0\). The authors obtain some closure properties of IFR(2) and NBU(2) random variables.