| Title:
|
Stability of characterizations of distribution functions using failure rate functions (English) |
| Author:
|
Koicheva, Maia |
| Author:
|
Omey, Edward |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
35 |
| Issue:
|
6 |
| Year:
|
1990 |
| Pages:
|
481-486 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
stability of characterizations |
| Keyword:
|
reliability theory |
| Keyword:
|
failure rate function |
| Keyword:
|
mean residual life distribution |
| MSC:
|
60E05 |
| MSC:
|
62E10 |
| MSC:
|
62N05 |
| idZBL:
|
Zbl 0727.62023 |
| idMR:
|
MR1089928 |
| DOI:
|
10.21136/AM.1990.104430 |
| . |
| Date available:
|
2008-05-20T18:40:23Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104430 |
| . |
| Reference:
|
[1] R. Barlow F. Proshan: Mathematical Theory of Reliability.John Wiley & Sons, New York, 1965. MR 0195566 |
| Reference:
|
[2] Manish C. Bhattarcharjee: On a characterization of a gamma distribution via exponential mixtures.J. Appl. Prob. 17 (2) 574-576, 1980. MR 0568970, 10.2307/3213049 |
| Reference:
|
[3] J. Galambos S. Kotz: Characterization of probability distributions.Lecture Notes in Mathematics, 675, 1978. MR 0513423 |
| Reference:
|
[4] R. C. Gupta J. P. Keating: Relations for reliability measures under length biased sampling.Scand. J. Statist. 13, 49-56, 1986. MR 0844034 |
| Reference:
|
[5] L. de Haan: On regular variation and its application to the weak convergence of sample extremes.Math. Centre Tracts 32, Amsterdam, 1970. Zbl 0226.60039, MR 0286156 |
| Reference:
|
[6] V. V. Kalashnikov S. T. Rachev: Characterization problems in queueing and their stability.Adv. Appl. Prob. 17, 868- 886, 1985. MR 0809434, 10.2307/1427091 |
| . |
