Bootstrapped confidence bands for percentile lifetime (Q1083822)

The (1-p) percentile residual lifetime is defined by \[ R(t,p)=Q(1-p(1- F(t)))-t,\quad 0\leq t<\infty \] where t is the lifetime, F(\(\cdot)\) is the life distribution function and \(Q(x)=\inf \{t>0:\) \(F(t)>x\}\) is the quantile function. An estimate of R(t,p) based on the empirical distribution function and empirical quantile function is suggested and their bootstrapped versions are used to construct a bootstrapped estimate and confidence bands. Results of a simulation study and a numerical example are presented.