Lifetime Distribution Classes
At the end of Chap.4, we introduced the IFR and DFR lifetime distribution classes based on the failure rate and residual life distribution. The IFR and DFR properties are quite strong as they require the full knowledge of residual life distribution F(x | t) = P[X ≤ t + x | X > t] for all t, x ≥ 0. In many practical situations, we may not need or have such full knowledge. For example, in reliability maintenance we may be only interested in the mean residual life to determine the maintenance schedule. In insurance mathematics, we may be only interested in the mean stop-and-loss claims. In this chapter, we shall introduce several lifetime distribution classes, which have gained wide applications in reliability, insurance, and economics. Since the notions are originated from reliability, so their main properties will be discussed from reliability terminology. More applications to other areas can be seen in later chapters.