# Article

Full entry | PDF   (0.9 MB)
Keywords:
stability of characterizations; reliability theory; failure rate function; mean residual life distribution
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. 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.
References:
[1] R. Barlow F. Proshan: Mathematical Theory of Reliability. John Wiley & Sons, New York, 1965. MR 0195566
[2] Manish C. Bhattarcharjee: On a characterization of a gamma distribution via exponential mixtures. J. Appl. Prob. 17 (2) 574-576, 1980. DOI 10.2307/3213049 | MR 0568970
[3] J. Galambos S. Kotz: Characterization of probability distributions. Lecture Notes in Mathematics, 675, 1978. MR 0513423
[4] R. C. Gupta J. P. Keating: Relations for reliability measures under length biased sampling. Scand. J. Statist. 13, 49-56, 1986. MR 0844034
[5] L. de Haan: On regular variation and its application to the weak convergence of sample extremes. Math. Centre Tracts 32, Amsterdam, 1970. MR 0286156 | Zbl 0226.60039
[6] V. V. Kalashnikov S. T. Rachev: Characterization problems in queueing and their stability. Adv. Appl. Prob. 17, 868- 886, 1985. DOI 10.2307/1427091 | MR 0809434

Partner of