By J.H. Fetzer

ISBN-10: 9027726078

ISBN-13: 9789027726070

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**Additional resources for Probability and Causality: Essays in Honor of Wesley C. Salmon **

**Sample text**

Yd) is said to be a survival Archimedean copula vector. 2 can be also formulated in terms of survival Archimedean copulas. 1 , we lose no generality by assuming that the marginal distributions are all the standard uniform U(O, 1). 1. Let (X1,X2, ... 3) with the standard uniform marginals. 4). Then for any n E {2, 3, . , d}, the vectors (XiI' Xi2 , ... , Xi n ) are Archimedean copula vectors with distribution functions n F n (X1,X2, .. ,xn) = B(L:R(Xi)), j=l X1,X2, .. 7) for all populations of indexes {iI, i2, ...

Bd). Introduce the partial ordering the following way. We say that a :S b if ai :S bi for all i = 1,2, ... ,d. A d-box is the Cartesian product of d closed intervals. For a :S b, we define the d-box [a, bl = {l E ~ : a :S l:S b} as the Cartesian product [aI, bll x [a2' b2 1 x ... x [ad, bdl and the vertices of [a, bl are the points iJ = (VI, V2, ... ,Vd) such that each Vm is equal to either am or bm . Introduce the following definitions. e. ai < bi for all i = 1,2, ... , d). Introduce the function sgnQ!

On TT-semigroups of probability distribution functions, II, Aequationes Mathematicae, 17, 19-40. 5. Kimberling, C. H. (1973). Exchangeable events and completely monotonic sequences, Rocky Mountain Journal of Mathematics, 3, 565-574. 6. Kimberling, C. H. (1974). A probabilistic interpretation of complete monotonicity, Aequationes Mathematicae, 10, 152-164. 7. Schweizer, B. and Sklar, A. (1983). Probabilistic Metric Spaces, Amsterdam: North-Holland. 8. Widder, D. V. (1946). The Laplace Transform, Princeton, New Jersey: Princeton University Press.

### Probability and Causality: Essays in Honor of Wesley C. Salmon by J.H. Fetzer

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