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  2. Extreme value theorem - Wikipedia

    en.wikipedia.org/wiki/Extreme_value_theorem

    The extreme value theorem was originally proven by Bernard Bolzano in the 1830s in a work Function Theory but the work remained unpublished until 1930. Bolzano's proof consisted of showing that a continuous function on a closed interval was bounded, and then showing that the function attained a maximum and a minimum value.

  3. Maximum and minimum - Wikipedia

    en.wikipedia.org/wiki/Maximum_and_minimum

    However, the normalised sinc function (blue) has arg min of {−1.43, 1.43}, approximately, because their global minima occur at x = ±1.43, even though the minimum value is the same. [7] In mathematics, the arguments of the maxima (abbreviated arg max or argmax) and arguments of the minima (abbreviated arg min or argmin) are the input points ...

  4. Arg max - Wikipedia

    en.wikipedia.org/wiki/Arg_max

    However, the normalised sinc function (blue) has arg min of {−1.43, 1.43}, approximately, because their global minima occur at x = ±1.43, even though the minimum value is the same. [1] In mathematics, the arguments of the maxima (abbreviated arg max or argmax) and arguments of the minima (abbreviated arg min or argmin) are the input points ...

  5. Extreme point - Wikipedia

    en.wikipedia.org/wiki/Extreme_point

    In mathematics, an extreme point of a convex set in a real or complex vector space is a point in that does not lie in any open line segment joining two points of . In linear programming problems, an extreme point is also called vertex or corner point of S . {\displaystyle S.} [ 1 ]

  6. Gumbel distribution - Wikipedia

    en.wikipedia.org/wiki/Gumbel_distribution

    The standard Gumbel distribution is the case where = and = with cumulative distribution function = ()and probability density function = (+).In this case the mode is 0, the median is ⁡ (⁡ ()), the mean is (the Euler–Mascheroni constant), and the standard deviation is /

  7. Extreme value theory - Wikipedia

    en.wikipedia.org/wiki/Extreme_value_theory

    Extreme value theory or extreme value analysis (EVA) is the study of extremes in statistical distributions. It is widely used in many disciplines, such as structural engineering , finance , economics , earth sciences , traffic prediction, and geological engineering .

  8. Stationary point - Wikipedia

    en.wikipedia.org/wiki/Stationary_point

    The stationary points are the red circles. In this graph, they are all relative maxima or relative minima. The blue squares are inflection points.. In mathematics, particularly in calculus, a stationary point of a differentiable function of one variable is a point on the graph of the function where the function's derivative is zero.

  9. Fermat's theorem (stationary points) - Wikipedia

    en.wikipedia.org/wiki/Fermat's_theorem...

    Fermat's theorem gives only a necessary condition for extreme function values, as some stationary points are inflection points (not a maximum or minimum). The function's second derivative , if it exists, can sometimes be used to determine whether a stationary point is a maximum or minimum.