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stability of characterizations; reliability theory; failure rate function; mean residual life distribution
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. In this paper 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.
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