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Psychological statistics is application of formulas, theorems, numbers and laws to psychology. Statistical methods for psychology include development and application statistical theory and methods for modeling psychological data. These methods include psychometrics, factor analysis, experimental designs, and Bayesian statistics. The article ...
This is a generalization of the concept of strongly convex function; by taking () = we recover the definition of strong convexity. It is worth noting that some authors require the modulus ϕ {\displaystyle \phi } to be an increasing function, [ 17 ] but this condition is not required by all authors.
The classes of s-convex measures form a nested increasing family as s decreases to −∞" . or, equivalently {} {}.Thus, the collection of −∞-convex measures is the largest such class, whereas the 0-convex measures (the logarithmically concave measures) are the smallest class.
then is called strictly convex. [1]Convex functions are related to convex sets. Specifically, the function is convex if and only if its epigraph. A function (in black) is convex if and only if its epigraph, which is the region above its graph (in green), is a convex set.
Convexity (finance) - refers to non-linearities in a financial model. When the price of an underlying variable changes, the price of an output does not change linearly, but depends on the higher-order derivatives of the modeling function. Geometrically, the model is no longer flat but curved, and the degree of curvature is called the convexity.
Convex optimization can be used to model problems in a wide range of disciplines, such as automatic control systems, estimation and signal processing, communications and networks, electronic circuit design, [7]: 17 data analysis and modeling, finance, statistics (optimal experimental design), [21] and structural optimization, where the ...
In economics, convex preferences are an individual's ordering of various outcomes, typically with regard to the amounts of various goods consumed, with the property that, roughly speaking, "averages are better than the extremes".
This definition is equivalent to the definition of convex curves from support lines. Every convex curve, defined as a curve with a support line through each point, is a subset of the boundary of its own convex hull. Every connected subset of the boundary of a convex set has a support line through each of its points. [8] [9] [19]