In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept...

absolutely monotonic function and a completely monotonic function are two very closely related concepts. Both imply very strong monotonicity properties...

well the relationship between two variables can be described using a monotonic function. The Spearman correlation between two variables is equal to the Pearson...

mathematical functions Injective metric space – Type of metric space Monotonic function – Order-preserving mathematical function Univalent function – Mathematical...

{\displaystyle g:\mathbb {R} \to \mathbb {R} } be a monotonic function, then the resulting density function is f Y ( y ) = f X ( g − 1 ( y ) ) | d d y ( g...

}\left(1\wedge x\right)\mu (dx)<\infty .} Absolutely and completely monotonic functions and sequences S. N. Bernstein (1928). "Sur les fonctions absolument...

square function preserves the order of positive numbers: larger numbers have larger squares. In other words, the square is a monotonic function on the...

inputs. Strict monotonic function: preserves the given order. Real function: a function whose domain is real. Complex function: a function whose domain...

determined by reverse look up in the same table, since the logarithm is a monotonic function. The product and quotient of two positive numbers c and d were routinely...

sequence. This is a special case of the more general notion of a monotonic function. The terms nondecreasing and nonincreasing are often used in place...

object Monotonic function, a property of a mathematical function Monotonicity of entailment, a property of some logical systems Monotonically increasing...

be a complete lattice and let f : L → L be an order-preserving (monotonic) function w.r.t. ≤ . Then the set of fixed points of f in L forms a complete...

since it allows convex analysis to be used. Since squaring is a monotonic function of non-negative values, minimizing squared distance is equivalent...

mathematics, a real-valued function is called convex if the line segment between any two distinct points on the graph of the function lies above the graph between...

each point and exactly one inflection point. In general, a sigmoid function is monotonic, and has a first derivative which is bell shaped. Conversely, the...

concave function can be quasiconvex. For example, x ↦ log ⁡ ( x ) {\displaystyle x\mapsto \log(x)} is both concave and quasiconvex. Any monotonic function is...

value zero for x = 1, is a differentiable function called the natural logarithm. A real function f is monotonic in an interval if the sign of f ( x ) −...

arc length s is a differentiable monotonic function of the parameter t, and conversely that t is a monotonic function of s. Moreover, by changing, if needed...

privacy that a person achieves. Third, privacy is described as a non-monotonic function. More privacy is not necessarily better. A person seeks an optimal...

temperature ranges (negative thermal expansion). Temperature is a monotonic function of the average molecular kinetic energy of a substance. As energy...

sound approximation of the semantics of computer programs, based on monotonic functions over ordered sets, especially lattices. It can be viewed as a partial...

more than once, the function fails the horizontal line test and is not injective. Vertical line test Inverse function Monotonic function Stewart, James (2003)...

) or inverse distribution function. With reference to a continuous and strictly monotonic cumulative distribution function F X : R → [ 0 , 1 ] {\displaystyle...

and equivalence and often occurs in the context of inequality and monotonic functions. It is often attached to a technical term to indicate that the exclusive...

cubic function is strictly monotonic. See the figure for an example of the case Δ0 > 0. The inflection point of a function is where that function changes...

well the relationship between two variables can be described by a monotonic function. The Kendall tau rank correlation coefficient is a measure of the...

hereditary, monotone, or minor-closed if the function formalizing the invariant forms a monotonic function from the corresponding partial order on graphs...

Examples of non-monotonic queries are aggregation queries, or queries with set difference. Identifying whether a query is monotonic can be crucial for...

trigonometric function is monotonic, one can define an inverse function, and this defines inverse trigonometric functions as multivalued functions. To define...

preferences which are weakly monotonic but not strongly monotonic are those represented by a Leontief utility function. If an agent has monotone preferences...