Geometric disintegration and star-shaped distributions. (English) Zbl 1330.60028
Summary: Geometric and stochastic representations are derived for the big class of \(p\)-generalized elliptically contoured distributions, and (generalizing Cavalieri’s and Torricelli’s method of indivisibles in a non-Euclidean sense) a geometric disintegration method is established for deriving even more general star-shaped distributions. Applications to constructing non-concentric elliptically contoured and generalized von Mises distributions are presented.
MSC:
| 60E05 | Probability distributions: general theory |
| 60D05 | Geometric probability and stochastic geometry |
| 28A50 | Integration and disintegration of measures |
| 28A75 | Length, area, volume, other geometric measure theory |
| 51F99 | Metric geometry |
Keywords:
\(p\)-generalized elliptically contoured distributions; non-concentric elliptically contoured distributions; star-generalized von Mises distributions; \(p\)-generalized ellipsoids and ellipsoidal coordinates; stochastic random vector representation; geometric measure representation; star-generalized surface measure; star-generalized uniform distribution; intersection-proportion function; Ball number functionReferences:
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