Technical Note—When Does the βth Percentile Residual Life Function Determine the Distribution?
Barry C. Arnold, Patrick L. Brockett
Operations Research · 1983 · Volume 31 · Issue 2
Abstract
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 β 1 and β 2 percentile residual life functions does uniquely determine the distribution provided that β 1 and β 2 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.).
Keywords
564 characterization of distributions, 725 βth percentile residual life function
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