Stability of characterizations of distribution functions using failure rate functions. (English) Zbl 0727.62023

Summary: Let \(\lambda\) denote the failure rate function of the d.f. F and let \(\lambda_ 1\) denote the failure rate function of the mean residual life distribution. We characterize the distribution functions F for which \(\lambda_ 1=c\lambda\) and we estimate F when it is only known that \(\lambda_ 1/\lambda\) or \(\lambda_ 1-c\lambda\) is bounded.


62E10 Characterization and structure theory of statistical distributions
62N05 Reliability and life testing
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