Sharpening jensen's inequality
WebbReduce inequality within and among countries - United Nations Sustainable Development. Home. About. Goals. Take Action. Partnerships. News and Media. Learn more. UN 2024 Water Conference. WebbJensen’s inequality is covered in all major statistical textbooks such as Casella and Berger ( 2002, Section 4.7) and Wasserman ( 2013, Section 4.2) as a basic mathematical tool …
Sharpening jensen's inequality
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Webb3 sep. 2024 · In this study, we propose a new bound for Jensen's inequality. Under certain conditions, it is an ultimate bound equal to the Jensen gap. To the best of our … Webb10 nov. 2024 · Abstract and Figures In this study, we propose a new bound for Jensen's inequality. Under certain conditions, it is an ultimate bound equal to the Jensen gap. To …
Webb10 dec. 2024 · The main aim of this paper is to give an improvement of the recent result on the sharpness of the Jensen inequality. The results given here are obtained using … WebbThis paper proposes a new sharpened version of the Jensen's inequality. The proposed new bound is simple and insightful, is broadly applicable by imposing minimum …
WebbDive into the research topics of 'Sharpening Jensen's Inequality'. Together they form a unique fingerprint. Sort by Weight Alphabetically Mathematics. Jensen's inequality 74%. Power Mean 38%. Moment generating function 34%. Presentation 24%. Calculus 23%. Form 12%. Business & Economics. Jensen's Inequality 100%. Moment ... WebbThe main aim of this paper is to give an improvement of the recent result on the sharpness of the Jensen inequality. The results given here are obtained using different Green …
WebbThe widely used Jensen’s inequality for convex functions, attributed to Danish mathematician Johan Jensen, dates back to 1906[12]. The literature contains numerous bounds on the Jensen gap, defined as J (f,X ∼ P) = E[f (X)] − f (E[X]), where X is a random variable with distribution P, and the function f might be convex or nonconvex [20].
In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function. It was proved by Jensen in 1906, building on an earlier proof of the same inequality for doubly-differentiable functions by Otto Hölder … Visa mer The classical form of Jensen's inequality involves several numbers and weights. The inequality can be stated quite generally using either the language of measure theory or (equivalently) probability. In the … Visa mer Form involving a probability density function Suppose Ω is a measurable subset of the real line and f(x) is a non-negative function such that $${\displaystyle \int _{-\infty }^{\infty }f(x)\,dx=1.}$$ Visa mer • Jensen's Operator Inequality of Hansen and Pedersen. • "Jensen inequality", Encyclopedia of Mathematics, EMS Press, 2001 [1994] • Weisstein, Eric W. "Jensen's inequality". MathWorld. Visa mer Jensen's inequality can be proved in several ways, and three different proofs corresponding to the different statements above will be offered. Before embarking on these … Visa mer • Karamata's inequality for a more general inequality • Popoviciu's inequality • Law of averages • A proof without words of Jensen's inequality Visa mer earth testing report formatWebbJensen's inequality is an inequality involving convexity of a function. We first make the following definitions: A function is convex on an interval I I if the segment between any two points taken on its graph ( ( in I) I) lies above the graph. An example of a convex function is f (x)=x^2 f (x) = x2. A function is concave on an interval ct refaWebbSharpeningJensen’s Inequality J. G. Liao and Arthur Berg Division of Biostatistics and Bioinformatics Penn State University College of Medicine October 26, 2024 Abstract This … c# treeview with columnsWebb26 juli 2024 · Sharpening Jensen's Inequality J. G. Liao, Arthur Berg This paper proposes a new sharpened version of the Jensen's inequality. The proposed new bound is simple … ctreeview类WebbSharpening Jensen's Inequality J. Liao, Arthur Berg Mathematics The American Statistician 2024 Abstract This article proposes a new sharpened version of Jensen's inequality. The proposed new bound is simple and insightful, is broadly applicable by imposing minimum assumptions, and provides… Expand 50 PDF View 1 excerpt, references background ctre falcon firmwareWebbJensen's Inequality Continuous Form It Application Interpolation Result We give a refinement of the converse Hölder inequality for functionals using an interpolation result for Jensen’s inequality. Additionally, we obtain similar improvements of the converse of the Beckenbach inequality. ctrefiningWebbHowever, applying Jensen on log-sums in Ie and £(XIE» is not as straightforward. Some terms in these expressions involve negative log-sums and so Jensen is actually solving for an upper bound on those terms. If we want overall lower and upper bounds on Ie and £(XIE», we need to compute reverse-Jensen bounds. 5 Reverse-Jensen Bounds earth test meter