Bivariate gamma distribution as a life test model

Giri S. Lingappaiah

Aplikace matematiky (1984)

  • Volume: 29, Issue: 3, page 182-188
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Lingappaiah, Giri S.. "Bivariate gamma distribution as a life test model." Aplikace matematiky 29.3 (1984): 182-188. <http://eudml.org/doc/15346>.

@article{Lingappaiah1984,
abstract = {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.},
author = {Lingappaiah, Giri S.},
journal = {Aplikace matematiky},
keywords = {bivariate gamma distribution; life test model; series system; dependent components; reliability; estimates; Bayesian approach; table; mean; variance; bivariate gamma distribution; life test model; series system; dependent components; reliability; Estimates; Bayesian approach; table; mean; variance},
language = {eng},
number = {3},
pages = {182-188},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Bivariate gamma distribution as a life test model},
url = {http://eudml.org/doc/15346},
volume = {29},
year = {1984},
}

TY - JOUR
AU - Lingappaiah, Giri S.
TI - Bivariate gamma distribution as a life test model
JO - Aplikace matematiky
PY - 1984
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 29
IS - 3
SP - 182
EP - 188
AB - 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.
LA - eng
KW - bivariate gamma distribution; life test model; series system; dependent components; reliability; estimates; Bayesian approach; table; mean; variance; bivariate gamma distribution; life test model; series system; dependent components; reliability; Estimates; Bayesian approach; table; mean; variance
UR - http://eudml.org/doc/15346
ER -

References

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  2. S. D. Al-Saadi D. H. Young, 10.1080/00949658008810386, Journal of Statistical Computation and Simulation, Vol. 11 (1980), 13-20. (1980) DOI10.1080/00949658008810386
  3. F. Downton, Bivariate exponential distribution in reliability theory, Journal of Royal Statistical Society-B, Vol. 32 (1970), 408-417. (1970) MR0287652
  4. E. J. Gumbel, 10.1080/01621459.1960.10483368, Journal of American Statistical Association, Vol. 55 (1960), 698-707. (1960) Zbl0099.14501MR0116403DOI10.1080/01621459.1960.10483368
  5. J. F. Lawless, 10.1080/00401706.1971.10488844, Technometrics, Vol. 13 (1971), 725-730. (1971) DOI10.1080/00401706.1971.10488844
  6. G. S. Lingappaiah, 10.2307/3314650.o, Canadian Journal of Statistics, Vol. 1 (1973), 113-117. (1973) Zbl0334.62042MR0400599DOI10.2307/3314650.o
  7. G. S. Lingappaiah, 10.1111/j.1467-842X.1974.tb00910.x, The Australian Journal of Statistics, Vol. 16 (1974), 30-32. (1974) Zbl0318.62080MR0365975DOI10.1111/j.1467-842X.1974.tb00910.x
  8. G. S. Lingappaiah, 10.1080/03610927908827839, Communications in Statistics, Vol. A8 (1979), 1403-1424. (1979) Zbl0416.62073MR0547405DOI10.1080/03610927908827839
  9. G. S. Lingappaiah, Intermittent life testing and Bayesian approach to prediction with spacings in the exponential model, STATISTICA, Vol. 40 (1980), 477-490. (1980) Zbl0472.62101MR0612467
  10. S. P. Mukherjee B. C. Samsal, Life distributions of coherent dependent systems, Journal of Indian Statistical Association, Vol. 26 (1977), 39-52. (1977) 
  11. P. A. P. Moran, 10.1093/biomet/56.3.627, Biometrika, Vol. 56 (1969), 627-634. (1969) MR0254948DOI10.1093/biomet/56.3.627
  12. D. Vere-Jones, The infinite divisibility of a bivariate gamma distribution, Sankhya-A, Vol. 29 (1967), 421-422. (1967) MR0226704

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