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Divergences Induced by the Cumulant and Partition Functions of Exponential Families and Their Deformations Induced by Comparative Convexity [PDF]
EntropyExponential families are statistical models which are the workhorses in statistics, information theory, and machine learning, among others. An exponential family can either be normalized subtractively by its cumulant or free energy function, or ...
Frank Nielsen
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Generalized Levinson's inequality and exponential convexity [PDF]
Opuscula Mathematica, 2015 We give a probabilistic version of Levinson's inequality under Mercer's assumption of equal variances for the family of 3-convex functions at a point.
Josip Pečarić +2 more
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Some Hadamard-Type Integral Inequalities Involving Modified Harmonic Exponential Type Convexity
Axioms, 2023 The term convexity and theory of inequalities is an enormous and intriguing domain of research in the realm of mathematical comprehension. Due to its applications in multiple areas of science, the theory of convexity and inequalities have recently ...
Asif Ali Shaikh +4 more
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Heliyon, 2020 In this paper, the idea and its algebraic properties of n–polynomial exponential type p–convex function have been investigated. Authors prove new trapezium type inequality for this new class of functions.
Saad Ihsan Butt +5 more
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Geometric Properties and Hardy Spaces of Rabotnov Fractional Exponential Functions
Fractal and Fractional, 2023 The aim of this study is to investigate a certain sufficiency criterion for uniform convexity, strong starlikeness, and strong convexity of Rabtonov fractional exponential functions. We also study the starlikeness and convexity of order γ.
Mohsan Raza +5 more
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Exponential type convexity and some related inequalities
Journal of Inequalities and Applications, 2020 In this manuscript, we give and study the concept of exponential type convex functions and some of their algebraic properties. We prove two Hermite–Hadamard (H-H) type integral inequalities for the newly introduced class of functions. We also obtain some
Mahir Kadakal, İmdat İşcan
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Media Statistika, 2017 Macaulay duration has often been used as a measure of the bond prices sensitivity to changes in interest rates. For a small change in interest rates, the duration provides a good approximation of the actual change in price.
Di Asih I Maruddani, Abdul Hoyyi
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Positive Semidefinite Matrices, Exponential Convexity for Majorization, and Related Cauchy Means
Journal of Inequalities and Applications, 2010 We prove positive semidefiniteness of matrices generated by differences deduced from majorization-type results which implies exponential convexity and log-convexity of these differences and also obtain Lyapunov's and Dresher's inequalities for these ...
Latif N, Pečarić J, Anwar M
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Positivity of Integrals for Higher Order $\nabla-$Convex and Completely Monotonic Functions [PDF]
Sahand Communications in Mathematical Analysis, 2022 We extend the definitions of $\nabla-$convex and completely monotonic functions for two variables. Some general identities of Popoviciu type integrals $\int P(y)f(y) dy$ and $\int \int P(y,z) f(y,z) dy dz$ are deduced.
Faraz Mehmood, Asif Khan, Muhammad Adnan
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Risks, 2023 Log-concavity and log-convexity play a key role in various scientific fields, especially in those where the distinction between exponential and non-exponential distributions is necessary for inferential purposes.
Alex Karagrigoriou +3 more
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