| Title:
|
Bivariate gamma distribution as a life test model (English) |
| Author:
|
Lingappaiah, Giri S. |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
29 |
| Issue:
|
3 |
| Year:
|
1984 |
| Pages:
|
182-188 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
The bivariate gamma distribution is taken as a life test model to analyse a series system with two dependent components $x$ and $y$. First, the distribution of a function of $x$ and $y$, that is, minimum $(x,y)$, is obtained. Next, the reliability of the component system is evaluated and tabulated for various values of the parameters. Estimates of the parameters are also obtained by using Bayesian approach. Finally, a table of the mean and variance of minimum $(x,y)$ for various values of the parameters involved is presented. (English) |
| Keyword:
|
bivariate gamma distribution |
| Keyword:
|
life test model |
| Keyword:
|
series system |
| Keyword:
|
dependent components |
| Keyword:
|
reliability |
| Keyword:
|
estimates |
| Keyword:
|
Bayesian approach |
| Keyword:
|
table |
| Keyword:
|
mean |
| Keyword:
|
variance |
| MSC:
|
62H10 |
| MSC:
|
62N05 |
| idZBL:
|
Zbl 0549.62065 |
| idMR:
|
MR0747210 |
| DOI:
|
10.21136/AM.1984.104083 |
| . |
| Date available:
|
2008-05-20T18:24:43Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104083 |
| . |
| Reference:
|
[1] S. D. Al-Saadi D. F. Serimshaw D. H. Young: Tests for independence of exponential variables.Journal of Statistical Computation and Simulation, Vol. 9 (1979), 217-233. MR 0539879, 10.1080/00949657908810318 |
| Reference:
|
[2] S. D. Al-Saadi D. H. Young: Estimators for the correlation coefficient in a bivariate exponential distribution.Journal of Statistical Computation and Simulation, Vol. 11 (1980), 13-20. 10.1080/00949658008810386 |
| Reference:
|
[3] F. Downton: Bivariate exponential distribution in reliability theory.Journal of Royal Statistical Society-B, Vol. 32 (1970), 408-417. MR 0287652 |
| Reference:
|
[4] E. J. Gumbel: Bivariate exponential distributions.Journal of American Statistical Association, Vol. 55 (1960), 698-707. Zbl 0099.14501, MR 0116403, 10.1080/01621459.1960.10483368 |
| Reference:
|
[5] J. F. Lawless: A prediction problem concerning samples from the exponential disribution with application to life testing.Technometrics, Vol. 13 (1971), 725-730. 10.1080/00401706.1971.10488844 |
| Reference:
|
[7] G. S. Lingappaiah: Prediction in exponential life testing.Canadian Journal of Statistics, Vol. 1 (1973), 113-117. Zbl 0334.62042, MR 0400599, 10.2307/3314650.o |
| Reference:
|
[7b] G. S. Lingappaiah: Prediction in samples from the gamma distribution as applied to life testing.The Australian Journal of Statistics, Vol. 16 (1974), 30-32. Zbl 0318.62080, MR 0365975, 10.1111/j.1467-842X.1974.tb00910.x |
| Reference:
|
[8] G. S. Lingappaiah: Bayesian approach to the prediction problem in complete and censored samples from the gamma and exponential populations.Communications in Statistics, Vol. A8 (1979), 1403-1424. Zbl 0416.62073, MR 0547405, 10.1080/03610927908827839 |
| Reference:
|
[9] G. S. Lingappaiah: Intermittent life testing and Bayesian approach to prediction with spacings in the exponential model.STATISTICA, Vol. 40 (1980), 477-490. Zbl 0472.62101, MR 0612467 |
| Reference:
|
[10] S. P. Mukherjee B. C. Samsal: Life distributions of coherent dependent systems.Journal of Indian Statistical Association, Vol. 26 (1977), 39-52. |
| Reference:
|
[11] P. A. P. Moran: Statistical inference in bivariate gamma distributions.Biometrika, Vol. 56 (1969), 627-634. MR 0254948, 10.1093/biomet/56.3.627 |
| Reference:
|
[12] D. Vere-Jones: The infinite divisibility of a bivariate gamma distribution.Sankhya-A, Vol. 29 (1967), 421-422. MR 0226704 |
| . |
