Lingappaiah, G. S. Bivariate gamma distribution as a life test model. (English) Zbl 0549.62065 Apl. Mat. 29, 182-188 (1984). 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. Cited in 3 Documents MSC: 62N05 Reliability and life testing 62H10 Multivariate distribution of statistics Keywords:bivariate gamma distribution; life test model; series system; dependent components; reliability; Estimates; Bayesian approach; table; mean; variance PDF BibTeX XML Cite \textit{G. S. Lingappaiah}, Apl. Mat. 29, 182--188 (1984; Zbl 0549.62065) Full Text: EuDML References: [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. · Zbl 0422.62088 [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. · Zbl 0453.62039 [3] F. Downton: Bivariate exponential distribution in reliability theory. Journal of Royal Statistical Society-B, Vol. 32 (1970), 408-417. · Zbl 0226.62101 [4] E. J. Gumbel: Bivariate exponential distributions. Journal of American Statistical Association, Vol. 55 (1960), 698-707. · Zbl 0099.14501 [5] J. F. Lawless: A prediction problem concerning samples from the exponential disribution with application to life testing. Technometrics, Vol. 13 (1971), 725-730. · Zbl 0223.62109 [6] G. S. Lingappaiah: Prediction in exponential life testing. Canadian Journal of Statistics, Vol. 1 (1973), 113-117. · Zbl 0334.62042 [7] 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 [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 [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 [10] S. P. Mukherjee B. C. Samsal: Life distributions of coherent dependent systems. Journal of Indian Statistical Association, Vol. 26 (1977), 39-52. · Zbl 0398.62079 [11] P. A. P. Moran: Statistical inference in bivariate gamma distributions. Biometrika, Vol. 56 (1969), 627-634. · Zbl 0184.42702 [12] D. Vere-Jones: The infinite divisibility of a bivariate gamma distribution. Sankhya-A, Vol. 29 (1967), 421-422. · Zbl 1204.60023 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.