A bivariate geometric distribution with applications to reliability. (English) Zbl 1162.62005

Krishna, Hare; Pundir, Pramendra Singh

Commun. Stat., Theory Methods 38, No. 7, 1079-1093 (2009).

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.

MSC:

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

Keywords:

Bayes estimation; Bayes risk; bivariate Dirichlet distribution; bivariate geometric distribution; maximum likelihood estimation

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