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The Lancaster’s Probabilities on R2 and Their Extreme Points

In: Distributions with given Marginals and Moment Problems

Author

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  • Gérard Letac

    (Université Paul Sabatier, Laboratoire de Statistique et Probabilités)

Abstract

Given two probabilities μ and ν on R, the Lancaster’s probabilities on R 2 are the probabilities $$\sigma (dx, dy)= \mu (dx) K (x, dy) = \nu (dy) L(y, dx)$$ with margins μ and ν such that for all $$n \epsilon N, \int_R y^n(x, dy)$$ and $$ \int_R y^n L(x, dy)$$ are polynomials with degree less or equal to n. This lecture reviews the properties of the convex set of these measures.

Suggested Citation

  • Gérard Letac, 1997. "The Lancaster’s Probabilities on R2 and Their Extreme Points," Springer Books, in: Viktor Beneš & Josef Štěpán (ed.), Distributions with given Marginals and Moment Problems, pages 179-190, Springer.
    • Handle: RePEc:spr:sprchp:978-94-011-5532-8_21
    DOI: 10.1007/978-94-011-5532-8_21
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