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A bivariate geometric distribution with applications to reliability. (English) Zbl 1162.62005
Summary: This article studies a bivariate geometric distribution (BGD) as a plausible reliability model. Maximum likelihood and Bayes estimators of parameters and various reliability characteristics are obtained. Approximations to the mean, variance, and Bayes risk of these estimators have been derived using Taylor expansions. A Monte-Carlo simulation study has been performed to compare these estimators. At the end, the theory is illustrated with a real data set example of accidents.

62E10 Characterization and structure theory of statistical distributions
62N02 Estimation in survival analysis and censored data
62N05 Reliability and life testing
65C05 Monte Carlo methods
62F15 Bayesian inference
62H05 Characterization and structure theory for multivariate probability distributions; copulas
Full Text: DOI Link
[1] DOI: 10.2307/3001656 · doi:10.2307/3001656
[2] Asha G., J. Ind. Statist. Assoc. 40 pp 1– (2002)
[3] Ayinde K., Sci. World J. 2 pp 21– (2007)
[4] Downton F., JRSS B 32 pp 408– (1970)
[5] Freeman M. F., Ann. Mathemat. Statist. 27 pp 601– (1950)
[6] Gibbons J. D., Nonparametric Statistical Inference (1971) · Zbl 0223.62050
[7] Hogg R. V., Introduction to Mathematical Statistics., 6. ed. (2005)
[8] Kocherlakota S., Bivariate Discrete Distributions (1992) · Zbl 0794.62002
[9] Phatak A. G., J. Ind. Statist. Assoc. 19 pp 141– (1981)
[10] DOI: 10.1006/jmva.1993.1065 · Zbl 0778.62092 · doi:10.1006/jmva.1993.1065
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