## 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.

### MSC:

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

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