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...

{\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...

Absolutely and completely monotonic functions and sequences Levin, Vladimir (1 March 1999). "Abstract Cyclical Monotonicity and Monge Solutions for the...

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

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...

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

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...

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

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

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

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

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 ) −...

different orthographies: el-monoton for monotonic Greek. el-polyton for polytonic Greek. While the tónos of monotonic orthography looks similar to the oxeîa...

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...

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

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

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

MR 2356043. Gelbaum, Bernard R.; Olmsted, John M. H. (1964), "18: A monotonic function whose points of discontinuity form an arbitrary countable (possibly...

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

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

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...

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

ISBN 978-3-540-44141-0, Zbl 1014.11015 Salem, Raphaël (1943), "On some singular monotonic functions which are strictly increasing" (PDF), Transactions of the American...

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...

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

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

{\displaystyle f(x)=0} almost everywhere. If f : [a, b] → R is a monotonic function, then f is differentiable almost everywhere. If f : R → R is Lebesgue...

{\displaystyle m=0} , the digamma function, ψ ( x ) = ψ ( 0 ) ( x ) {\displaystyle \psi (x)=\psi ^{(0)}(x)} , is strictly monotonic increasing and strictly concave...

model Multinomial probit Q–Q plot Continuous function Monotonic function Quantile function Sigmoid function Rankit analysis, also developed by Chester Bliss...