9.13 Conclusion
In this chapter, we present several concepts of multivariate dependence, in particular bivariate positive dependence. While there does not appear to have relationship between the traditional concepts of dependence and ageing concepts, there is a strong relationship between positive dependence and rank correlations such as Kendall’s τ and Spearman’s ρS. Also the relationship between these two non-parametric measures of association can be interpreted by positive dependence concepts such as PQD and LTD, RTI. (PQD implies 3τ ≥ ρS ≥ 0; whereas simultaneous LTD and RTI implies 3τ ≥ ρS ≥ τ ≥ 0).
Although the concept of local dependence and measure of local dependence are not fully developed yet, they would likely provide us more information about the dependence between two time intervals as in the medical studies example mentioned in the last section.
Keywords
- Bivariate Distribution
- Local Dependence
- Bivariate Normal Distribution
- Positive Dependence
- Dependence Concept
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Rights and permissions
Copyright information
© 2006 Springer Science+Business Media, Inc.
About this chapter
Cite this chapter
(2006). Concepts and Measures of Dependence in Reliability. In: Stochastic Ageing and Dependence for Reliability. Springer, New York, NY. https://doi.org/10.1007/0-387-34232-X_9
Download citation
DOI: https://doi.org/10.1007/0-387-34232-X_9
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-29742-2
Online ISBN: 978-0-387-34232-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)