Multivariate Unimodality
نویسندگان
چکیده
منابع مشابه
On strong unimodality of multivariate discrete distributions
A discrete function f defined on Zn is said to be logconcave if f(λx+(1− λ)y) ≥ [f(x)]λ[f(y)]1−λ for x, y, λx + (1− λ)y ∈ Zn. A more restrictive notion is strong unimodality. Following Barndorff-Nielsen (1973) a discrete function p(z), z ∈ Zn is called strongly unimodal if there exists a convex function f(x), x ∈ Rn such that f(x) = − log p(x), if x ∈ Zn. In this paper sufficient conditions are...
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Let P (x) be a unimodal polynomial of degree m with nonnegative coefficients and a mode n for nonnegative integers n m. We study the unimodality of P (x+ z) for real numbers z = 1 or z 2 and show that: if z = 1, P (x + z) is unimodal provided that m − n 4; if z 2, then P (x+ z) is unimodal provided that m− n 2z + 1; and we also show that the given conditions are best possible. Additionally, we ...
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 1976
ISSN: 0090-5364
DOI: 10.1214/aos/1176343466