# Stability of characterizations of distribution functions using failure rate functions

Aplikace matematiky (1990)

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

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topKoicheva, 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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- J. Galambos S. Kotz, Characterization of probability distributions, Lecture Notes in Mathematics, 675, 1978. (1978) MR0513423
- R. C. Gupta J. P. Keating, Relations for reliability measures under length biased sampling, Scand. J. Statist. 13, 49-56, 1986. (1986) MR0844034
- 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
- V. V. Kalashnikov S. T. Rachev, 10.2307/1427091, Adv. Appl. Prob. 17, 868- 886, 1985. (1985) MR0809434DOI10.2307/1427091

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