Stability of characterizations of distribution functions using failure rate functions

Maia Koicheva; Edward Omey

Aplikace matematiky (1990)

  • Volume: 35, Issue: 6, page 481-486
  • ISSN: 0862-7940

Abstract

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Let λ denote the failure rate function of the d , f . F and let λ 1 denote the failure rate function of the mean residual life distribution. In this paper we characterize the distribution functions F for which λ 1 = c λ and we estimate F when it is only known that λ 1 / λ or λ 1 - c λ is bounded.

How to cite

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Koicheva, Maia, and Omey, Edward. "Stability of characterizations of distribution functions using failure rate functions." Aplikace matematiky 35.6 (1990): 481-486. <http://eudml.org/doc/15648>.

@article{Koicheva1990,
abstract = {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.},
author = {Koicheva, Maia, Omey, Edward},
journal = {Aplikace matematiky},
keywords = {stability of characterizations; reliability theory; failure rate function; mean residual life distribution; stability of characterizations; reliability theory; failure rate function; mean residual life distribution},
language = {eng},
number = {6},
pages = {481-486},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Stability of characterizations of distribution functions using failure rate functions},
url = {http://eudml.org/doc/15648},
volume = {35},
year = {1990},
}

TY - JOUR
AU - Koicheva, Maia
AU - Omey, Edward
TI - Stability of characterizations of distribution functions using failure rate functions
JO - Aplikace matematiky
PY - 1990
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 35
IS - 6
SP - 481
EP - 486
AB - 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.
LA - eng
KW - stability of characterizations; reliability theory; failure rate function; mean residual life distribution; stability of characterizations; reliability theory; failure rate function; mean residual life distribution
UR - http://eudml.org/doc/15648
ER -

References

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  1. R. Barlow F. Proshan, Mathematical Theory of Reliability, John Wiley & Sons, New York, 1965. (1965) MR0195566
  2. Manish C. Bhattarcharjee, 10.2307/3213049, J. Appl. Prob. 17 (2) 574-576, 1980. (1980) MR0568970DOI10.2307/3213049
  3. J. Galambos S. Kotz, Characterization of probability distributions, Lecture Notes in Mathematics, 675, 1978. (1978) MR0513423
  4. R. C. Gupta J. P. Keating, Relations for reliability measures under length biased sampling, Scand. J. Statist. 13, 49-56, 1986. (1986) MR0844034
  5. L. de Haan, On regular variation and its application to the weak convergence of sample extremes, Math. Centre Tracts 32, Amsterdam, 1970. (1970) Zbl0226.60039MR0286156
  6. V. V. Kalashnikov S. T. Rachev, 10.2307/1427091, Adv. Appl. Prob. 17, 868- 886, 1985. (1985) MR0809434DOI10.2307/1427091

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