Knowledge of the βth percentile residual life function does not uniquely determine the underlying distribution. Additional information about the tail behavior of the distribution is needed. Knowledge of both the β1 and β2 percentile residual life functions does uniquely determine the distribution provided that β1 and β2 are noncommensurate. This corrects and extends the results of Schmittlein and Morrison (Schmittlein, D. C., D. G. Morrison. 1981. The median residual lifetime; a characterization theorem and an application. Opns. Res. 29 392–399.).
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Arnold et al. (1983) studied this question.
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