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In mathematical analysis, the maximum and minimum[ a ] of a function are, respectively, the largest and smallest value taken by the function. Known generically as extremum, [ b ] they may be defined either within a given range (the local or relative extrema) or on the entire domain (the global or absolute extrema) of a function. [ 1 ][ 2 ][ 3 ...
The sample maximum and minimum are the least robust statistics: they are maximally sensitive to outliers.. This can either be an advantage or a drawback: if extreme values are real (not measurement errors), and of real consequence, as in applications of extreme value theory such as building dikes or financial loss, then outliers (as reflected in sample extrema) are important.
Minimax (sometimes Minmax, MM[ 1] or saddle point[ 2]) is a decision rule used in artificial intelligence, decision theory, game theory, statistics, and philosophy for minimizing the possible loss for a worst case ( max imum loss) scenario. When dealing with gains, it is referred to as "maximin" – to maximize the minimum gain.
Extreme value theorem. A continuous function on the closed interval showing the absolute max (red) and the absolute min (blue). In calculus, the extreme value theorem states that if a real-valued function is continuous on the closed and bounded interval , then must attain a maximum and a minimum, each at least once.
The Appraisal Institute defines highest and best use as follows: The reasonably probable and legal use of vacant land or an improved property that is physically possible, appropriately supported, financially feasible, and that results in the highest value. The four criteria the highest and best use must meet are legal permissibility, physical ...
The maximum theorem provides conditions for the continuity of an optimized function and the set of its maximizers with ... is the maximized value of the function ...
Arg max. As an example, both unnormalised and normalised sinc functions above have of {0} because both attain their global maximum value of 1 at x = 0. The unnormalised sinc function (red) has arg min of {−4.49, 4.49}, approximately, because it has 2 global minimum values of approximately −0.217 at x = ±4.49.
Maximum principle. In the mathematical fields of differential equations and geometric analysis, the maximum principle is one of the most useful and best known tools of study. Solutions of a differential inequality in a domain D satisfy the maximum principle if they achieve their maxima at the boundary of D . The maximum principle enables one to ...