Abstract
Two basic ideas that give rise to global dependence stochastic orders were introduced and studied in Shaked et al. (Methodology and Computing in Applied Probability 14:617–648, 2012). Here these are reviewed, and two new ideas that give rise to new global dependence orders are then brought out and discussed. Two particular global dependence orders that come up from the two new general ideas are studied in detail. It is shown, among other things, how these orders can be identified and verified. In particular, conditions on the underlying copulas that yield these global dependence orders are given. The theory is illustrated by some examples. It is shown that some global dependence measures are preserved by the new global dependence orders. An application in reliability theory illustrates the usefulness of the new global dependence orders.
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Shaked, M., Sordo, M.A., Suárez-Llorens, A. (2013). A Global Dependence Stochastic Order Based on the Presence of Noise. In: Li, H., Li, X. (eds) Stochastic Orders in Reliability and Risk. Lecture Notes in Statistics(), vol 208. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6892-9_1
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DOI: https://doi.org/10.1007/978-1-4614-6892-9_1
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