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stability of characterizations; reliability theory; failure rate function; mean residual life distribution

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