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...

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

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

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...

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

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

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

and exactly 1/4 at the inflection point. In general, a sigmoid function is monotonic, and has a first derivative which is bell shaped. Conversely, the...

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...

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

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...

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

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

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 ) −...

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

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

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

derivative test, according to which the monotonicity of a function can be defined as the inequality of function's first derivative greater or less than...

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...

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

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

in the previous argument. On the other hand, even though general monotonic functions are differentiable almost everywhere, the proof of the general formula...

) or inverse distribution function. With reference to a continuous and strictly monotonic cumulative distribution function (c.d.f.) F X : R → [ 0 , 1...

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

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

FFD(S,C)} is not a monotonic function of C. : Fig.4  Similarly, F F D ( S , C ) {\displaystyle FFD(S,C)} is not a monotonic function of the sizes of items...

{\displaystyle [\mathbf {x} ]} . Interval functions beyond the four basic operators may also be defined. For monotonic functions in one variable, the range of values...