= New better than used in expectation
{title2=$\int_x^\infty\overline F_X(t)\,dt\le\mu\overline F_X(x)$}
= NBUE
{c}
{synonym}
A nonnegative lifetime or claim law is new better than used in expectation if its <mean residual life> at every age with positive survival is at most its original mean. The displayed equivalent inequality says that its <equilibrium claim-size distribution> is no larger in <stochastic order> than the original law. For an <Erlang distribution> of shape two and rate one, the two survival functions are $(1+x/2)e^{-x}$ and $(1+x)e^{-x}$, so the condition holds.
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