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A function that is not monotonic. In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. [ 1 ][ 2 ][ 3 ] This concept first arose in calculus, and was later generalized to the more abstract setting of order theory.
In the mathematical field of real analysis, the monotone convergence theorem is any of a number of related theorems proving the good convergence behaviour of monotonic sequences, i.e. sequences that are non- increasing, or non- decreasing. In its simplest form, it says that a non-decreasing bounded -above sequence of real numbers converges to ...
Interval arithmetic (also known as interval mathematics;interval analysis or interval computation) is a mathematical technique used to mitigate rounding and measurement errors in mathematical computation by computing function bounds. Numerical methods involving interval arithmetic can guarantee relatively reliable and mathematically correct ...
In probability and statistics, the quantile function outputs the value of a random variable such that its probability is less than or equal to an input probability value. Intuitively, the quantile function associates with a range at and below a probability input the likelihood that a random variable is realized in that range for some ...
If p is a probability, then p/(1 − p) is the corresponding odds; the logit of the probability is the logarithm of the odds, i.e.: = = = = (). The base of the logarithm function used is of little importance in the present article, as long as it is greater than 1, but the natural logarithm with base e is the one most often used.
In constrained optimizationin economics, the shadow price is the change, per infinitesimalunit of the constraint, in the optimal value of the objective function of an optimization problemobtained by relaxing the constraint. If the objective function is utility, it is the marginal utilityof relaxing the constraint.
In probability theory and statistics, the probit function is the quantile function associated with the standard normal distribution. It has applications in data analysis and machine learning, in particular exploratory statistical graphics and specialized regression modeling of binary response variables. Mathematically, the probit is the inverse ...
In mathematics, the total variation identifies several slightly different concepts, related to the (local or global) structure of the codomain of a function or a measure.For a real-valued continuous function f, defined on an interval [a, b] ⊂ R, its total variation on the interval of definition is a measure of the one-dimensional arclength of the curve with parametric equation x ↦ f(x ...